8x^2+x=-x+15

Solution for 8x^2+x=-x+15 equation:

8x^2+x=-x+15

We move all terms to the left:

8x^2+x-(-x+15)=0

We add all the numbers together, and all the variables

8x^2+x-(-1x+15)=0

We get rid of parentheses

8x^2+x+1x-15=0

We add all the numbers together, and all the variables

8x^2+2x-15=0

a = 8; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·8·(-15)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*8}=\frac{-24}{16}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*8}=\frac{20}{16}
=1+1/4
$