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

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

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

We move all terms to the left:

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

We multiply parentheses

4x^2-12x-(2x+6)=0

We get rid of parentheses

4x^2-12x-2x-6=0

We add all the numbers together, and all the variables

4x^2-14x-6=0

a = 4; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·4·(-6)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*4}=\frac{14-2\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*4}=\frac{14+2\sqrt{73}}{8}
$