4x(2x-3)=6x+2

Solution for 4x(2x-3)=6x+2 equation:

4x(2x-3)=6x+2

We move all terms to the left:

4x(2x-3)-(6x+2)=0

We multiply parentheses

8x^2-12x-(6x+2)=0

We get rid of parentheses

8x^2-12x-6x-2=0

We add all the numbers together, and all the variables

8x^2-18x-2=0

a = 8; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·8·(-2)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{97}}{2*8}=\frac{18-2\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{97}}{2*8}=\frac{18+2\sqrt{97}}{16}
$