X^2-90x+150=0

Solution for X^2-90x+150=0 equation:

X^2-90X+150=0

a = 1; b = -90; c = +150;
Δ = b2-4ac
Δ = -902-4·1·150
Δ = 7500
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:

$\sqrt{\Delta}=\sqrt{7500}=\sqrt{2500*3}=\sqrt{2500}*\sqrt{3}=50\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-50\sqrt{3}}{2*1}=\frac{90-50\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+50\sqrt{3}}{2*1}=\frac{90+50\sqrt{3}}{2}
$