(12x+36)/(x+4)=x+3

Solution for (12x+36)/(x+4)=x+3 equation:

(12x+36)/(x+4)=x+3

We move all terms to the left:

(12x+36)/(x+4)-(x+3)=0


Domain of the equation: (x+4)!=0

We move all terms containing x to the left, all other terms to the right

x!=-4

x∈R


We get rid of parentheses

(12x+36)/(x+4)-x-3=0

We multiply all the terms by the denominator


(12x+36)-x*(x+4)-3*(x+4)=0

We multiply parentheses

-x^2+(12x+36)-4x-3x-12=0

We get rid of parentheses

-x^2+12x-4x-3x+36-12=0

We add all the numbers together, and all the variables

-1x^2+5x+24=0

a = -1; b = 5; c = +24;
Δ = b2-4ac
Δ = 52-4·(-1)·24
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{-(5)-11}{2*-1}=\frac{-16}{-2}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-1}=\frac{6}{-2}
=-3
$