6x^2-78x+132=0

Solution for 6x^2-78x+132=0 equation:

6x^2-78x+132=0

a = 6; b = -78; c = +132;
Δ = b2-4ac
Δ = -782-4·6·132
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-54}{2*6}=\frac{24}{12}
=2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+54}{2*6}=\frac{132}{12}
=11
$