12x^2+54x-108=0

Solution for 12x^2+54x-108=0 equation:

12x^2+54x-108=0

a = 12; b = 54; c = -108;
Δ = b2-4ac
Δ = 542-4·12·(-108)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-90}{2*12}=\frac{-144}{24}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+90}{2*12}=\frac{36}{24}
=1+1/2
$