4x^2-90x+180=0

Solution for 4x^2-90x+180=0 equation:

4x^2-90x+180=0

a = 4; b = -90; c = +180;
Δ = b2-4ac
Δ = -902-4·4·180
Δ = 5220
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:

$\sqrt{\Delta}=\sqrt{5220}=\sqrt{36*145}=\sqrt{36}*\sqrt{145}=6\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{145}}{2*4}=\frac{90-6\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{145}}{2*4}=\frac{90+6\sqrt{145}}{8}
$