4x^2-144x+144=0

Solution for 4x^2-144x+144=0 equation:

4x^2-144x+144=0

a = 4; b = -144; c = +144;
Δ = b2-4ac
Δ = -1442-4·4·144
Δ = 18432
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:

$\sqrt{\Delta}=\sqrt{18432}=\sqrt{9216*2}=\sqrt{9216}*\sqrt{2}=96\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-96\sqrt{2}}{2*4}=\frac{144-96\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+96\sqrt{2}}{2*4}=\frac{144+96\sqrt{2}}{8}
$