3/w-7+3/w=3w-18/w-7

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

3/w-7+3/w=3w-18/w-7

We move all terms to the left:

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


Domain of the equation: w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3w*w+24=0

Wy multiply elements

-3w^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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$w_{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}
$
$w_{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}
$