x^2-65x-78^2=0

Solution for x^2-65x-78^2=0 equation:

x^2-65x-78^2=0

We add all the numbers together, and all the variables

x^2-65x-6084=0

a = 1; b = -65; c = -6084;
Δ = b2-4ac
Δ = -652-4·1·(-6084)
Δ = 28561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28561}=169$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-65)-169}{2*1}=\frac{-104}{2}
=-52
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+169}{2*1}=\frac{234}{2}
=117
$