15x^2+27x-81=255

Solution for 15x^2+27x-81=255 equation:

15x^2+27x-81=255

We move all terms to the left:

15x^2+27x-81-(255)=0

We add all the numbers together, and all the variables

15x^2+27x-336=0

a = 15; b = 27; c = -336;
Δ = b2-4ac
Δ = 272-4·15·(-336)
Δ = 20889
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:

$\sqrt{\Delta}=\sqrt{20889}=\sqrt{9*2321}=\sqrt{9}*\sqrt{2321}=3\sqrt{2321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{2321}}{2*15}=\frac{-27-3\sqrt{2321}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{2321}}{2*15}=\frac{-27+3\sqrt{2321}}{30}
$