(2x+6)(4x-1)-6x^2+54=0

Solution for (2x+6)(4x-1)-6x^2+54=0 equation:

(2x+6)(4x-1)-6x^2+54=0

We multiply parentheses ..

-6x^2+(+8x^2-2x+24x-6)+54=0

We get rid of parentheses

-6x^2+8x^2-2x+24x-6+54=0

We add all the numbers together, and all the variables

2x^2+22x+48=0

a = 2; b = 22; c = +48;
Δ = b2-4ac
Δ = 222-4·2·48
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-10}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+10}{2*2}=\frac{-12}{4}
=-3
$