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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-14x-4=0

a = 4; b = -14; c = -4;
Δ = b2-4ac
Δ = -142-4·4·(-4)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{65}}{2*4}=\frac{14-2\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{65}}{2*4}=\frac{14+2\sqrt{65}}{8}
$