(2x-60)x=90

Solution for (2x-60)x=90 equation:

(2x-60)x=90

We move all terms to the left:

(2x-60)x-(90)=0

We multiply parentheses

2x^2-60x-90=0

a = 2; b = -60; c = -90;
Δ = b2-4ac
Δ = -602-4·2·(-90)
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{30}}{2*2}=\frac{60-12\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{30}}{2*2}=\frac{60+12\sqrt{30}}{4}
$