4x(5x-30)=30

Solution for 4x(5x-30)=30 equation:

4x(5x-30)=30

We move all terms to the left:

4x(5x-30)-(30)=0

We multiply parentheses

20x^2-120x-30=0

a = 20; b = -120; c = -30;
Δ = b2-4ac
Δ = -1202-4·20·(-30)
Δ = 16800
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:

$\sqrt{\Delta}=\sqrt{16800}=\sqrt{400*42}=\sqrt{400}*\sqrt{42}=20\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-20\sqrt{42}}{2*20}=\frac{120-20\sqrt{42}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+20\sqrt{42}}{2*20}=\frac{120+20\sqrt{42}}{40}
$