8x2=6x-x2

Solution for 8x2=6x-x2 equation:

8x^2=6x-x2

We move all terms to the left:

8x^2-(6x-x2)=0

We add all the numbers together, and all the variables

8x^2-(+6x-1x^2)=0

We get rid of parentheses

8x^2+1x^2-6x=0

We add all the numbers together, and all the variables

9x^2-6x=0

a = 9; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·9·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*9}=\frac{12}{18}
=2/3
$