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5x^2=-80+40x

5x^2=-80+40x equation

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Numerical solution:

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The solution

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5*x  = -80 + 40*x
5x2=40x−805 x^{2} = 40 x - 80
Simplify
Detail solution
Move right part of the equation to
left part with negative sign.

The equation is transformed from
5x2=40x−805 x^{2} = 40 x - 80
to
5x2−(40x−80)=05 x^{2} - \left(40 x - 80\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=5a = 5
b=−40b = -40
c=80c = 80
, then
D=b2−4 a c=D = b^2 - 4\ a\ c =
(−1)5⋅4⋅80+(−40)2=0\left(-1\right) 5 \cdot 4 \cdot 80 + \left(-40\right)^{2} = 0
Because D = 0, then the equation has one root.
x = -b/2a = --40/2/(5)

x1=4x_{1} = 4
Vieta's Theorem
rewrite the equation
5x2=40x−805 x^{2} = 40 x - 80
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
x2−8x+16=0x^{2} - 8 x + 16 = 0
px+x2+q=0p x + x^{2} + q = 0
where
p=bap = \frac{b}{a}
p=−8p = -8
q=caq = \frac{c}{a}
q=16q = 16
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=8x_{1} + x_{2} = 8
x1x2=16x_{1} x_{2} = 16
The graph
02468-6-4-2141012-200200
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x_1 = 4
x1=4x_{1} = 4
Simplify
Sum and product of roots [src] 
sum
4
(4)\left(4\right) 
=
4
44
Simplify 
product
4
(4)\left(4\right) 
=
4
44
Simplify
Numerical answer [src] 
x1 = 4.0
x1 = 4.0
The graph
5x^2=-80+40x equation
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