x2+x+7=9x2+x-1

Solution for x2+x+7=9x2+x-1 equation:

x2+x+7=9x^2+x-1

We move all terms to the left:

x2+x+7-(9x^2+x-1)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2+8=0

a = -8; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-8)·8
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*-8}=\frac{-16}{-16}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*-8}=\frac{16}{-16}
=-1
$