4x^2-72x+81=0

Solution for 4x^2-72x+81=0 equation:

4x^2-72x+81=0

a = 4; b = -72; c = +81;
Δ = b2-4ac
Δ = -722-4·4·81
Δ = 3888
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-36\sqrt{3}}{2*4}=\frac{72-36\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+36\sqrt{3}}{2*4}=\frac{72+36\sqrt{3}}{8}
$