(12x^2-68x+72)=0

Solution for (12x^2-68x+72)=0 equation:

(12x^2-68x+72)=0

We get rid of parentheses

12x^2-68x+72=0

a = 12; b = -68; c = +72;
Δ = b2-4ac
Δ = -682-4·12·72
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{73}}{2*12}=\frac{68-4\sqrt{73}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{73}}{2*12}=\frac{68+4\sqrt{73}}{24}
$