4x(x-6)=150

Solution for 4x(x-6)=150 equation:

4x(x-6)=150

We move all terms to the left:

4x(x-6)-(150)=0

We multiply parentheses

4x^2-24x-150=0

a = 4; b = -24; c = -150;
Δ = b2-4ac
Δ = -242-4·4·(-150)
Δ = 2976
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:

$\sqrt{\Delta}=\sqrt{2976}=\sqrt{16*186}=\sqrt{16}*\sqrt{186}=4\sqrt{186}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{186}}{2*4}=\frac{24-4\sqrt{186}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{186}}{2*4}=\frac{24+4\sqrt{186}}{8}
$