4x^2-90x+60=0

Solution for 4x^2-90x+60=0 equation:

4x^2-90x+60=0

a = 4; b = -90; c = +60;
Δ = b2-4ac
Δ = -902-4·4·60
Δ = 7140
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:

$\sqrt{\Delta}=\sqrt{7140}=\sqrt{4*1785}=\sqrt{4}*\sqrt{1785}=2\sqrt{1785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1785}}{2*4}=\frac{90-2\sqrt{1785}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1785}}{2*4}=\frac{90+2\sqrt{1785}}{8}
$