12x^2-4x=20

Solution for 12x^2-4x=20 equation:

12x^2-4x=20

We move all terms to the left:

12x^2-4x-(20)=0

a = 12; b = -4; c = -20;
Δ = b2-4ac
Δ = -42-4·12·(-20)
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{61}}{2*12}=\frac{4-4\sqrt{61}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{61}}{2*12}=\frac{4+4\sqrt{61}}{24}
$