(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 get rid of parentheses

-6x^2+(2x+6)(4x-1)-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-60=0

a = 2; b = 22; c = -60;
Δ = b2-4ac
Δ = 222-4·2·(-60)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{241}}{2*2}=\frac{-22-2\sqrt{241}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{241}}{2*2}=\frac{-22+2\sqrt{241}}{4}
$