x(2x-255)=180

Solution for x(2x-255)=180 equation:

x(2x-255)=180

We move all terms to the left:

x(2x-255)-(180)=0

We multiply parentheses

2x^2-255x-180=0

a = 2; b = -255; c = -180;
Δ = b2-4ac
Δ = -2552-4·2·(-180)
Δ = 66465
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:

$\sqrt{\Delta}=\sqrt{66465}=\sqrt{9*7385}=\sqrt{9}*\sqrt{7385}=3\sqrt{7385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-255)-3\sqrt{7385}}{2*2}=\frac{255-3\sqrt{7385}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-255)+3\sqrt{7385}}{2*2}=\frac{255+3\sqrt{7385}}{4}
$