X2-90x-1800=0

Solution for X2-90x-1800=0 equation:

X2-90X-1800=0

We add all the numbers together, and all the variables

X^2-90X-1800=0

a = 1; b = -90; c = -1800;
Δ = b2-4ac
Δ = -902-4·1·(-1800)
Δ = 15300
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:

$\sqrt{\Delta}=\sqrt{15300}=\sqrt{900*17}=\sqrt{900}*\sqrt{17}=30\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{17}}{2*1}=\frac{90-30\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{17}}{2*1}=\frac{90+30\sqrt{17}}{2}
$