3(x+2)4x-7=15

Solution for 3(x+2)4x-7=15 equation:

3(x+2)4x-7=15

We move all terms to the left:

3(x+2)4x-7-(15)=0

We add all the numbers together, and all the variables

3(x+2)4x-22=0

We multiply parentheses

12x^2+24x-22=0

a = 12; b = 24; c = -22;
Δ = b2-4ac
Δ = 242-4·12·(-22)
Δ = 1632
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:

$\sqrt{\Delta}=\sqrt{1632}=\sqrt{16*102}=\sqrt{16}*\sqrt{102}=4\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{102}}{2*12}=\frac{-24-4\sqrt{102}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{102}}{2*12}=\frac{-24+4\sqrt{102}}{24}
$