6x+2x(x+3)=3x+5x+6

Solution for 6x+2x(x+3)=3x+5x+6 equation:

6x+2x(x+3)=3x+5x+6

We move all terms to the left:

6x+2x(x+3)-(3x+5x+6)=0

We add all the numbers together, and all the variables

6x+2x(x+3)-(8x+6)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+4x-6=0

a = 2; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·2·(-6)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*2}=\frac{4}{4}
=1
$