12x^2-72x=-56

Solution for 12x^2-72x=-56 equation:

12x^2-72x=-56

We move all terms to the left:

12x^2-72x-(-56)=0

We add all the numbers together, and all the variables

12x^2-72x+56=0

a = 12; b = -72; c = +56;
Δ = b2-4ac
Δ = -722-4·12·56
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{-(-72)-8\sqrt{39}}{2*12}=\frac{72-8\sqrt{39}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{39}}{2*12}=\frac{72+8\sqrt{39}}{24}
$