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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

10x-(x^2+x+7)-1=0

We get rid of parentheses

-x^2+10x-x-7-1=0

We add all the numbers together, and all the variables

-1x^2+9x-8=0

a = -1; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·(-1)·(-8)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-1}=\frac{-2}{-2}
=1
$