x^2-90x-175=0

Solution for x^2-90x-175=0 equation:

x^2-90x-175=0

a = 1; b = -90; c = -175;
Δ = b2-4ac
Δ = -902-4·1·(-175)
Δ = 8800
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:

$\sqrt{\Delta}=\sqrt{8800}=\sqrt{400*22}=\sqrt{400}*\sqrt{22}=20\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-20\sqrt{22}}{2*1}=\frac{90-20\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+20\sqrt{22}}{2*1}=\frac{90+20\sqrt{22}}{2}
$