6x^2-76x+180=0

Solution for 6x^2-76x+180=0 equation:

6x^2-76x+180=0

a = 6; b = -76; c = +180;
Δ = b2-4ac
Δ = -762-4·6·180
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-4\sqrt{91}}{2*6}=\frac{76-4\sqrt{91}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+4\sqrt{91}}{2*6}=\frac{76+4\sqrt{91}}{12}
$