(2x+3)(4x-12)=4

Solution for (2x+3)(4x-12)=4 equation:

(2x+3)(4x-12)=4

We move all terms to the left:

(2x+3)(4x-12)-(4)=0

We multiply parentheses ..

(+8x^2-24x+12x-36)-4=0

We get rid of parentheses

8x^2-24x+12x-36-4=0

We add all the numbers together, and all the variables

8x^2-12x-40=0

a = 8; b = -12; c = -40;
Δ = b2-4ac
Δ = -122-4·8·(-40)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{89}}{2*8}=\frac{12-4\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{89}}{2*8}=\frac{12+4\sqrt{89}}{16}
$