12x^2-7(12x)=-12

Solution for 12x^2-7(12x)=-12 equation:

12x^2-7(12x)=-12

We move all terms to the left:

12x^2-7(12x)-(-12)=0

We add all the numbers together, and all the variables

12x^2-712x+12=0

a = 12; b = -712; c = +12;
Δ = b2-4ac
Δ = -7122-4·12·12
Δ = 506368
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:

$\sqrt{\Delta}=\sqrt{506368}=\sqrt{256*1978}=\sqrt{256}*\sqrt{1978}=16\sqrt{1978}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-712)-16\sqrt{1978}}{2*12}=\frac{712-16\sqrt{1978}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-712)+16\sqrt{1978}}{2*12}=\frac{712+16\sqrt{1978}}{24}
$