8x^2+12x-11=6+x

Solution for 8x^2+12x-11=6+x equation:

8x^2+12x-11=6+x

We move all terms to the left:

8x^2+12x-11-(6+x)=0

We add all the numbers together, and all the variables

8x^2+12x-(x+6)-11=0

We get rid of parentheses

8x^2+12x-x-6-11=0

We add all the numbers together, and all the variables

8x^2+11x-17=0

a = 8; b = 11; c = -17;
Δ = b2-4ac
Δ = 112-4·8·(-17)
Δ = 665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{665}}{2*8}=\frac{-11-\sqrt{665}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{665}}{2*8}=\frac{-11+\sqrt{665}}{16}
$