2(2x^2+3x-54)=0

Solution for 2(2x^2+3x-54)=0 equation:

2(2x^2+3x-54)=0

We multiply parentheses

4x^2+6x-108=0

a = 4; b = 6; c = -108;
Δ = b2-4ac
Δ = 62-4·4·(-108)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-42}{2*4}=\frac{-48}{8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+42}{2*4}=\frac{36}{8}
=4+1/2
$