36x2+48x+16=12

Solution for 36x2+48x+16=12 equation:

36x^2+48x+16=12

We move all terms to the left:

36x^2+48x+16-(12)=0

We add all the numbers together, and all the variables

36x^2+48x+4=0

a = 36; b = 48; c = +4;
Δ = b2-4ac
Δ = 482-4·36·4
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{3}}{2*36}=\frac{-48-24\sqrt{3}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{3}}{2*36}=\frac{-48+24\sqrt{3}}{72}
$