5x(4x-12)=42

Solution for 5x(4x-12)=42 equation:

5x(4x-12)=42

We move all terms to the left:

5x(4x-12)-(42)=0

We multiply parentheses

20x^2-60x-42=0

a = 20; b = -60; c = -42;
Δ = b2-4ac
Δ = -602-4·20·(-42)
Δ = 6960
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:

$\sqrt{\Delta}=\sqrt{6960}=\sqrt{16*435}=\sqrt{16}*\sqrt{435}=4\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{435}}{2*20}=\frac{60-4\sqrt{435}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{435}}{2*20}=\frac{60+4\sqrt{435}}{40}
$