12x(13x+16)=20

Solution for 12x(13x+16)=20 equation:

12x(13x+16)=20

We move all terms to the left:

12x(13x+16)-(20)=0

We multiply parentheses

156x^2+192x-20=0

a = 156; b = 192; c = -20;
Δ = b2-4ac
Δ = 1922-4·156·(-20)
Δ = 49344
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:

$\sqrt{\Delta}=\sqrt{49344}=\sqrt{64*771}=\sqrt{64}*\sqrt{771}=8\sqrt{771}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-8\sqrt{771}}{2*156}=\frac{-192-8\sqrt{771}}{312}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+8\sqrt{771}}{2*156}=\frac{-192+8\sqrt{771}}{312}
$