(x+9)(x+3)/(x-7)(x+1)=4

Solution for (x+9)(x+3)/(x-7)(x+1)=4 equation:

(x+9)(x+3)/(x-7)(x+1)=4

We move all terms to the left:

(x+9)(x+3)/(x-7)(x+1)-(4)=0


Domain of the equation: (x-7)(x+1)!=0

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

x-7)(x!=-1

x∈R


We multiply parentheses ..

(+x^2+3x+9x+27)/(x-7)(x+1)-4=0

We multiply all the terms by the denominator


(+x^2+3x+9x+27)-4*(x-7)(x+1)=0

We get rid of parentheses

x^2+3x+9x-4*(x-7)(x+1)+27=0

We multiply parentheses ..

x^2-4*(+x^2+x-7x-7)+3x+9x+27=0

We add all the numbers together, and all the variables

x^2-4*(+x^2+x-7x-7)+12x+27=0

We multiply parentheses

x^2-4x^2-4x+28x+12x+28+27=0

We add all the numbers together, and all the variables

-3x^2+36x+55=0

a = -3; b = 36; c = +55;
Δ = b2-4ac
Δ = 362-4·(-3)·55
Δ = 1956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1956}=\sqrt{4*489}=\sqrt{4}*\sqrt{489}=2\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{489}}{2*-3}=\frac{-36-2\sqrt{489}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{489}}{2*-3}=\frac{-36+2\sqrt{489}}{-6}
$