6x^2+18x-225=0

Solution for 6x^2+18x-225=0 equation:

6x^2+18x-225=0

a = 6; b = 18; c = -225;
Δ = b2-4ac
Δ = 182-4·6·(-225)
Δ = 5724
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:

$\sqrt{\Delta}=\sqrt{5724}=\sqrt{36*159}=\sqrt{36}*\sqrt{159}=6\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{159}}{2*6}=\frac{-18-6\sqrt{159}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{159}}{2*6}=\frac{-18+6\sqrt{159}}{12}
$