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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-1x-7=0

a = 8; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·8·(-7)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*8}=\frac{-14}{16}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*8}=\frac{16}{16}
=1
$