-7a^2+72a-72=0

Solution for -7a^2+72a-72=0 equation:

-7a^2+72a-72=0

a = -7; b = 72; c = -72;
Δ = b2-4ac
Δ = 722-4·(-7)·(-72)
Δ = 3168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3168}=\sqrt{144*22}=\sqrt{144}*\sqrt{22}=12\sqrt{22}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{22}}{2*-7}=\frac{-72-12\sqrt{22}}{-14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{22}}{2*-7}=\frac{-72+12\sqrt{22}}{-14}
$