6w^2-78w+72=0

Solution for 6w^2-78w+72=0 equation:

6w^2-78w+72=0

a = 6; b = -78; c = +72;
Δ = b2-4ac
Δ = -782-4·6·72
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-66}{2*6}=\frac{12}{12}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+66}{2*6}=\frac{144}{12}
=12
$