9x^2+x-1=x^2+x+17

Solution for 9x^2+x-1=x^2+x+17 equation:

9x^2+x-1=x^2+x+17

We move all terms to the left:

9x^2+x-1-(x^2+x+17)=0

We get rid of parentheses

9x^2-x^2+x-x-17-1=0

We add all the numbers together, and all the variables

8x^2-18=0

a = 8; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·8·(-18)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*8}=\frac{-24}{16}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*8}=\frac{24}{16}
=1+1/2
$