9x^2-27x=15

Solution for 9x^2-27x=15 equation:

9x^2-27x=15

We move all terms to the left:

9x^2-27x-(15)=0

a = 9; b = -27; c = -15;
Δ = b2-4ac
Δ = -272-4·9·(-15)
Δ = 1269
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:

$\sqrt{\Delta}=\sqrt{1269}=\sqrt{9*141}=\sqrt{9}*\sqrt{141}=3\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{141}}{2*9}=\frac{27-3\sqrt{141}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{141}}{2*9}=\frac{27+3\sqrt{141}}{18}
$