x*(5x-50)=150

Solution for x*(5x-50)=150 equation:

x(5x-50)=150

We move all terms to the left:

x(5x-50)-(150)=0

We multiply parentheses

5x^2-50x-150=0

a = 5; b = -50; c = -150;
Δ = b2-4ac
Δ = -502-4·5·(-150)
Δ = 5500
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:

$\sqrt{\Delta}=\sqrt{5500}=\sqrt{100*55}=\sqrt{100}*\sqrt{55}=10\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{55}}{2*5}=\frac{50-10\sqrt{55}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{55}}{2*5}=\frac{50+10\sqrt{55}}{10}
$