4x(2x+1)=12

Solution for 4x(2x+1)=12 equation:

4x(2x+1)=12

We move all terms to the left:

4x(2x+1)-(12)=0

We multiply parentheses

8x^2+4x-12=0

a = 8; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·8·(-12)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*8}=\frac{-24}{16}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*8}=\frac{16}{16}
=1
$