x(3x-15)=150

Solution for x(3x-15)=150 equation:

x(3x-15)=150

We move all terms to the left:

x(3x-15)-(150)=0

We multiply parentheses

3x^2-15x-150=0

a = 3; b = -15; c = -150;
Δ = b2-4ac
Δ = -152-4·3·(-150)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-45}{2*3}=\frac{-30}{6}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+45}{2*3}=\frac{60}{6}
=10
$