X(2x-225)=180

Solution for X(2x-225)=180 equation:

X(2X-225)=180

We move all terms to the left:

X(2X-225)-(180)=0

We multiply parentheses

2X^2-225X-180=0

a = 2; b = -225; c = -180;
Δ = b2-4ac
Δ = -2252-4·2·(-180)
Δ = 52065
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:

$\sqrt{\Delta}=\sqrt{52065}=\sqrt{9*5785}=\sqrt{9}*\sqrt{5785}=3\sqrt{5785}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-225)-3\sqrt{5785}}{2*2}=\frac{225-3\sqrt{5785}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-225)+3\sqrt{5785}}{2*2}=\frac{225+3\sqrt{5785}}{4}
$