12x(2x+2)=20

Solution for 12x(2x+2)=20 equation:

12x(2x+2)=20

We move all terms to the left:

12x(2x+2)-(20)=0

We multiply parentheses

24x^2+24x-20=0

a = 24; b = 24; c = -20;
Δ = b2-4ac
Δ = 242-4·24·(-20)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-8\sqrt{39}}{2*24}=\frac{-24-8\sqrt{39}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{39}}{2*24}=\frac{-24+8\sqrt{39}}{48}
$