X2-150x+225=0

Solution for X2-150x+225=0 equation:

X2-150X+225=0

We add all the numbers together, and all the variables

X^2-150X+225=0

a = 1; b = -150; c = +225;
Δ = b2-4ac
Δ = -1502-4·1·225
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-60\sqrt{6}}{2*1}=\frac{150-60\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+60\sqrt{6}}{2*1}=\frac{150+60\sqrt{6}}{2}
$