3/x+3/x-7=3x-18/x-7

Solution for 3/x+3/x-7=3x-18/x-7 equation:

3/x+3/x-7=3x-18/x-7

We move all terms to the left:

3/x+3/x-7-(3x-18/x-7)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

3/x+3/x-3x+18/x+7-7=0

We multiply all the terms by the denominator


-3x*x+7*x-7*x+3+3+18=0

We add all the numbers together, and all the variables

-3x*x+24=0

Wy multiply elements

-3x^2+24=0

a = -3; b = 0; c = +24;
Δ = b2-4ac
Δ = 02-4·(-3)·24
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-3}=\frac{0-12\sqrt{2}}{-6}
=-\frac{12\sqrt{2}}{-6}
=-\frac{2\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-3}=\frac{0+12\sqrt{2}}{-6}
=\frac{12\sqrt{2}}{-6}
=\frac{2\sqrt{2}}{-1}
$