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+10x+6=0

a = 4; b = 10; c = +6;
Δ = b2-4ac
Δ = 102-4·4·6
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*4}=\frac{-8}{8}
=-1
$