2x^2+3x=6-8x

Solution for 2x^2+3x=6-8x equation:

2x^2+3x=6-8x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2+3x+8x-6=0

We add all the numbers together, and all the variables

2x^2+11x-6=0

a = 2; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·2·(-6)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*2}=\frac{2}{4}
=1/2
$