X^2-8x-27=-x-9

Solution for X^2-8x-27=-x-9 equation:

X^2-8X-27=-X-9

We move all terms to the left:

X^2-8X-27-(-X-9)=0

We add all the numbers together, and all the variables

X^2-8X-(-1X-9)-27=0

We get rid of parentheses

X^2-8X+1X+9-27=0

We add all the numbers together, and all the variables

X^2-7X-18=0

a = 1; b = -7; c = -18;
Δ = b2-4ac
Δ = -72-4·1·(-18)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*1}=\frac{-4}{2}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*1}=\frac{18}{2}
=9
$