X2-76x-71=0

Solution for X2-76x-71=0 equation:

X2-76X-71=0

We add all the numbers together, and all the variables

X^2-76X-71=0

a = 1; b = -76; c = -71;
Δ = b2-4ac
Δ = -762-4·1·(-71)
Δ = 6060
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6060}=\sqrt{4*1515}=\sqrt{4}*\sqrt{1515}=2\sqrt{1515}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1515}}{2*1}=\frac{76-2\sqrt{1515}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1515}}{2*1}=\frac{76+2\sqrt{1515}}{2}
$