2x^2+6x=2+3x

Solution for 2x^2+6x=2+3x equation:

2x^2+6x=2+3x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2+6x-3x-2=0

We add all the numbers together, and all the variables

2x^2+3x-2=0

a = 2; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·2·(-2)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*2}=\frac{2}{4}
=1/2
$