9x^2+x-1=x^2+1+7

Solution for 9x^2+x-1=x^2+1+7 equation:

9x^2+x-1=x^2+1+7

We move all terms to the left:

9x^2+x-1-(x^2+1+7)=0

We get rid of parentheses

9x^2-x^2+x-1-7-1=0

We add all the numbers together, and all the variables

8x^2+x-9=0

a = 8; b = 1; c = -9;
Δ = b2-4ac
Δ = 12-4·8·(-9)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*8}=\frac{-18}{16}
=-1+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*8}=\frac{16}{16}
=1
$