4a^2-36a+9=0

Solution for 4a^2-36a+9=0 equation:

4a^2-36a+9=0

a = 4; b = -36; c = +9;
Δ = b2-4ac
Δ = -362-4·4·9
Δ = 1152
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:

$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-24\sqrt{2}}{2*4}=\frac{36-24\sqrt{2}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+24\sqrt{2}}{2*4}=\frac{36+24\sqrt{2}}{8}
$