3/x+3/x+4=3x-9/x-4

Solution for 3/x+3/x+4=3x-9/x-4 equation:

3/x+3/x+4=3x-9/x-4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

3/x+3/x-3x+9/x+4+4=0

We multiply all the terms by the denominator


-3x*x+4*x+4*x+3+3+9=0

We add all the numbers together, and all the variables

8x-3x*x+15=0

Wy multiply elements

-3x^2+8x+15=0

a = -3; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·(-3)·15
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{61}}{2*-3}=\frac{-8-2\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{61}}{2*-3}=\frac{-8+2\sqrt{61}}{-6}
$