2x^2+6x-54=0

Solution for 2x^2+6x-54=0 equation:

2x^2+6x-54=0

a = 2; b = 6; c = -54;
Δ = b2-4ac
Δ = 62-4·2·(-54)
Δ = 468
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:

$\sqrt{\Delta}=\sqrt{468}=\sqrt{36*13}=\sqrt{36}*\sqrt{13}=6\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{13}}{2*2}=\frac{-6-6\sqrt{13}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{13}}{2*2}=\frac{-6+6\sqrt{13}}{4}
$