20x-5x(6x+4)=4x-6

Solution for 20x-5x(6x+4)=4x-6 equation:

20x-5x(6x+4)=4x-6

We move all terms to the left:

20x-5x(6x+4)-(4x-6)=0

We multiply parentheses

-30x^2+20x-20x-(4x-6)=0

We get rid of parentheses

-30x^2+20x-20x-4x+6=0

We add all the numbers together, and all the variables

-30x^2-4x+6=0

a = -30; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-30)·6
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*-30}=\frac{4-4\sqrt{46}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*-30}=\frac{4+4\sqrt{46}}{-60}
$