x2-90x-1200=0

Solution for x2-90x-1200=0 equation:

x2-90x-1200=0

We add all the numbers together, and all the variables

x^2-90x-1200=0

a = 1; b = -90; c = -1200;
Δ = b2-4ac
Δ = -902-4·1·(-1200)
Δ = 12900
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:

$\sqrt{\Delta}=\sqrt{12900}=\sqrt{100*129}=\sqrt{100}*\sqrt{129}=10\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-10\sqrt{129}}{2*1}=\frac{90-10\sqrt{129}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+10\sqrt{129}}{2*1}=\frac{90+10\sqrt{129}}{2}
$