12x^2+3x=6^2

Solution for 12x^2+3x=6^2 equation:

12x^2+3x=6^2

We move all terms to the left:

12x^2+3x-(6^2)=0

We add all the numbers together, and all the variables

12x^2+3x-36=0

a = 12; b = 3; c = -36;
Δ = b2-4ac
Δ = 32-4·12·(-36)
Δ = 1737
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:

$\sqrt{\Delta}=\sqrt{1737}=\sqrt{9*193}=\sqrt{9}*\sqrt{193}=3\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{193}}{2*12}=\frac{-3-3\sqrt{193}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{193}}{2*12}=\frac{-3+3\sqrt{193}}{24}
$