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4x^2-4x-15=0 equation

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Numerical solution:

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The solution

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4*x  - 4*x - 15 = 0
(4x2−4x)−15=0\left(4 x^{2} - 4 x\right) - 15 = 0
Simplify
Detail solution
This equation is of the form
a*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 = b^2 - 4*a*c - it is the discriminant.
Because
a=4a = 4
b=−4b = -4
c=−15c = -15
, then
D = b^2 - 4 * a * c = 

(-4)^2 - 4 * (4) * (-15) = 256

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
x1=52x_{1} = \frac{5}{2}
x2=−32x_{2} = - \frac{3}{2}
Vieta's Theorem
rewrite the equation
(4x2−4x)−15=0\left(4 x^{2} - 4 x\right) - 15 = 0
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−x−154=0x^{2} - x - \frac{15}{4} = 0
px+q+x2=0p x + q + x^{2} = 0
where
p=bap = \frac{b}{a}
p=−1p = -1
q=caq = \frac{c}{a}
q=−154q = - \frac{15}{4}
Vieta Formulas
x1+x2=−px_{1} + x_{2} = - p
x1x2=qx_{1} x_{2} = q
x1+x2=1x_{1} + x_{2} = 1
x1x2=−154x_{1} x_{2} = - \frac{15}{4}
The graph
05-15-10-51015-5001000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
-3/2 + 5/2
−32+52- \frac{3}{2} + \frac{5}{2} 
=
1
11 
product
-3*5
----
2*2
−154- \frac{15}{4} 
=
-15/4
−154- \frac{15}{4} 
-15/4
Rapid solution [src] 
x1 = -3/2
x1=−32x_{1} = - \frac{3}{2} 
x2 = 5/2
x2=52x_{2} = \frac{5}{2} 
x2 = 5/2
Numerical answer [src] 
x1 = -1.5
x2 = 2.5
x2 = 2.5
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