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2x^2+15-3x=11x-5

2x^2+15-3x=11x-5 equation

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Numerical solution:

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The solution

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2*x  + 15 - 3*x = 11*x - 5
2x2−3x+15=11x−52 x^{2} - 3 x + 15 = 11 x - 5
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
2x2−3x+15=11x−52 x^{2} - 3 x + 15 = 11 x - 5
to
(−11x+5)+(2x2−3x+15)=0\left(- 11 x + 5\right) + \left(2 x^{2} - 3 x + 15\right) = 0
This equation is of the form
a x2+b x+c=0a\ x^2 + b\ x + c = 0
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
x1=D−b2ax_{1} = \frac{\sqrt{D} - b}{2 a}
x2=−D−b2ax_{2} = \frac{- \sqrt{D} - b}{2 a}
where D=b2−4acD = b^2 - 4 a c is the discriminant.
Because
a=2a = 2
b=−14b = -14
c=20c = 20
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
(−1)2⋅4⋅20+(−14)2=36\left(-1\right) 2 \cdot 4 \cdot 20 + \left(-14\right)^{2} = 36
Because D > 0, then the equation has two roots.
x1=(−b+D)2ax_1 = \frac{(-b + \sqrt{D})}{2 a}
x2=(−b−D)2ax_2 = \frac{(-b - \sqrt{D})}{2 a}
or
x1=5x_{1} = 5
Simplify
x2=2x_{2} = 2
Simplify
Vieta's Theorem
rewrite the equation
2x2−3x+15=11x−52 x^{2} - 3 x + 15 = 11 x - 5
of
ax2+bx+c=0a x^{2} + b x + c = 0
as reduced quadratic equation
x2+bxa+ca=0x^{2} + \frac{b x}{a} + \frac{c}{a} = 0
x2−7x+10=0x^{2} - 7 x + 10 = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−7p = -7
q=caq = \frac{c}{a}
q=10q = 10
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=7x_{1} + x_{2} = 7
x1x2=10x_{1} x_{2} = 10
The graph
02468-8-6-4-2101214-200200
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
2 + 5
(2)+(5)\left(2\right) + \left(5\right) 
=
7
77
Simplify 
product
2 * 5
(2)∗(5)\left(2\right) * \left(5\right) 
=
10
1010
Simplify
Rapid solution [src] 
x_1 = 2
x1=2x_{1} = 2
Simplify 
x_2 = 5
x2=5x_{2} = 5
Simplify
Numerical answer [src] 
x1 = 5.0
x2 = 2.0
x2 = 2.0
The graph
2x^2+15-3x=11x-5 equation
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