9x^2-45x+15=0

Solution for 9x^2-45x+15=0 equation:

9x^2-45x+15=0

a = 9; b = -45; c = +15;
Δ = b2-4ac
Δ = -452-4·9·15
Δ = 1485
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:

$\sqrt{\Delta}=\sqrt{1485}=\sqrt{9*165}=\sqrt{9}*\sqrt{165}=3\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{165}}{2*9}=\frac{45-3\sqrt{165}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{165}}{2*9}=\frac{45+3\sqrt{165}}{18}
$