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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+2x-6=0

a = 4; b = 2; c = -6;
Δ = b2-4ac
Δ = 22-4·4·(-6)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*4}=\frac{8}{8}
=1
$