X2-90x-900=0

Solution for X2-90x-900=0 equation:

X2-90X-900=0

We add all the numbers together, and all the variables

X^2-90X-900=0

a = 1; b = -90; c = -900;
Δ = b2-4ac
Δ = -902-4·1·(-900)
Δ = 11700
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:

$\sqrt{\Delta}=\sqrt{11700}=\sqrt{900*13}=\sqrt{900}*\sqrt{13}=30\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{13}}{2*1}=\frac{90-30\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{13}}{2*1}=\frac{90+30\sqrt{13}}{2}
$