6x^2-52x+72=0

Solution for 6x^2-52x+72=0 equation:

6x^2-52x+72=0

a = 6; b = -52; c = +72;
Δ = b2-4ac
Δ = -522-4·6·72
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{61}}{2*6}=\frac{52-4\sqrt{61}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{61}}{2*6}=\frac{52+4\sqrt{61}}{12}
$