9x^2-90x+162=0

Solution for 9x^2-90x+162=0 equation:

9x^2-90x+162=0

a = 9; b = -90; c = +162;
Δ = b2-4ac
Δ = -902-4·9·162
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-18\sqrt{7}}{2*9}=\frac{90-18\sqrt{7}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+18\sqrt{7}}{2*9}=\frac{90+18\sqrt{7}}{18}
$