X^2+x-8^2=40^2

Solution for X^2+x-8^2=40^2 equation:

X^2+X-8^2=40^2

We move all terms to the left:

X^2+X-8^2-(40^2)=0

We add all the numbers together, and all the variables

X^2+X-1664=0

a = 1; b = 1; c = -1664;
Δ = b2-4ac
Δ = 12-4·1·(-1664)
Δ = 6657
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{6657}}{2*1}=\frac{-1-\sqrt{6657}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{6657}}{2*1}=\frac{-1+\sqrt{6657}}{2}
$