X^2-2x-47=9+8x

Solution for X^2-2x-47=9+8x equation:

X^2-2X-47=9+8X

We move all terms to the left:

X^2-2X-47-(9+8X)=0

We add all the numbers together, and all the variables

X^2-2X-(8X+9)-47=0

We get rid of parentheses

X^2-2X-8X-9-47=0

We add all the numbers together, and all the variables

X^2-10X-56=0

a = 1; b = -10; c = -56;
Δ = b2-4ac
Δ = -102-4·1·(-56)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18}{2*1}=\frac{-8}{2}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18}{2*1}=\frac{28}{2}
=14
$