(x-3)(x+4)=x+x-9

Solution for (x-3)(x+4)=x+x-9 equation:

(x-3)(x+4)=x+x-9

We move all terms to the left:

(x-3)(x+4)-(x+x-9)=0

We add all the numbers together, and all the variables

(x-3)(x+4)-(2x-9)=0

We get rid of parentheses

(x-3)(x+4)-2x+9=0

We multiply parentheses ..

(+x^2+4x-3x-12)-2x+9=0

We get rid of parentheses

x^2+4x-3x-2x-12+9=0

We add all the numbers together, and all the variables

x^2-1x-3=0

a = 1; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·1·(-3)
Δ = 13
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{-(-1)-\sqrt{13}}{2*1}=\frac{1-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{13}}{2*1}=\frac{1+\sqrt{13}}{2}
$