9a^2-48a+36=0

Solution for 9a^2-48a+36=0 equation:

9a^2-48a+36=0

a = 9; b = -48; c = +36;
Δ = b2-4ac
Δ = -482-4·9·36
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-12\sqrt{7}}{2*9}=\frac{48-12\sqrt{7}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+12\sqrt{7}}{2*9}=\frac{48+12\sqrt{7}}{18}
$