3w-5/w-3=2w-1

Solution for 3w-5/w-3=2w-1 equation:

3w-5/w-3=2w-1

We move all terms to the left:

3w-5/w-3-(2w-1)=0


Domain of the equation: w!=0

w∈R


We get rid of parentheses

3w-5/w-2w+1-3=0

We multiply all the terms by the denominator


3w*w-2w*w+1*w-3*w-5=0

We add all the numbers together, and all the variables

-2w+3w*w-2w*w-5=0

Wy multiply elements

3w^2-2w^2-2w-5=0

We add all the numbers together, and all the variables

w^2-2w-5=0

a = 1; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·1·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{6}}{2*1}=\frac{2-2\sqrt{6}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{6}}{2*1}=\frac{2+2\sqrt{6}}{2}
$