6x^2-90x+225=0

Solution for 6x^2-90x+225=0 equation:

6x^2-90x+225=0

a = 6; b = -90; c = +225;
Δ = b2-4ac
Δ = -902-4·6·225
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-30\sqrt{3}}{2*6}=\frac{90-30\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+30\sqrt{3}}{2*6}=\frac{90+30\sqrt{3}}{12}
$