4x^2+12x-54=0

Solution for 4x^2+12x-54=0 equation:

4x^2+12x-54=0

a = 4; b = 12; c = -54;
Δ = b2-4ac
Δ = 122-4·4·(-54)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{7}}{2*4}=\frac{-12-12\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{7}}{2*4}=\frac{-12+12\sqrt{7}}{8}
$