8x^2+4x+3x^2+4-3x=5x^2+8x+2

Solution for 8x^2+4x+3x^2+4-3x=5x^2+8x+2 equation:

8x^2+4x+3x^2+4-3x=5x^2+8x+2

We move all terms to the left:

8x^2+4x+3x^2+4-3x-(5x^2+8x+2)=0

We add all the numbers together, and all the variables

11x^2+x-(5x^2+8x+2)+4=0

We get rid of parentheses

11x^2-5x^2+x-8x-2+4=0

We add all the numbers together, and all the variables

6x^2-7x+2=0

a = 6; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·6·2
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-1}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+1}{2*6}=\frac{8}{12}
=2/3
$