X*x+x-9=2x+3

Solution for X*x+x-9=2x+3 equation:

X*X+X-9=2X+3

We move all terms to the left:

X*X+X-9-(2X+3)=0

We add all the numbers together, and all the variables

X+X*X-(2X+3)-9=0

Wy multiply elements

X^2+X-(2X+3)-9=0

We get rid of parentheses

X^2+X-2X-3-9=0

We add all the numbers together, and all the variables

X^2-1X-12=0

a = 1; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·1·(-12)
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{-(-1)-7}{2*1}=\frac{-6}{2}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*1}=\frac{8}{2}
=4
$