(x-12)(5x)=90

Solution for (x-12)(5x)=90 equation:

(x-12)(5x)=90

We move all terms to the left:

(x-12)(5x)-(90)=0

We multiply parentheses

5x^2-60x-90=0

a = 5; b = -60; c = -90;
Δ = b2-4ac
Δ = -602-4·5·(-90)
Δ = 5400
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:

$\sqrt{\Delta}=\sqrt{5400}=\sqrt{900*6}=\sqrt{900}*\sqrt{6}=30\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-30\sqrt{6}}{2*5}=\frac{60-30\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+30\sqrt{6}}{2*5}=\frac{60+30\sqrt{6}}{10}
$