X^2+8x-9=x

Solution for X^2+8x-9=x equation:

X^2+8X-9=X

We move all terms to the left:

X^2+8X-9-(X)=0

We add all the numbers together, and all the variables

X^2+7X-9=0

a = 1; b = 7; c = -9;
Δ = b2-4ac
Δ = 72-4·1·(-9)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{85}}{2*1}=\frac{-7-\sqrt{85}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*1}=\frac{-7+\sqrt{85}}{2}
$