2x(4x+3)=12

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

2x(4x+3)=12

We move all terms to the left:

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

We multiply parentheses

8x^2+6x-12=0

a = 8; b = 6; c = -12;
Δ = b2-4ac
Δ = 62-4·8·(-12)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*8}=\frac{-6-2\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*8}=\frac{-6+2\sqrt{105}}{16}
$