5w-3/w-2=6

Solution for 5w-3/w-2=6 equation:

5w-3/w-2=6

We move all terms to the left:

5w-3/w-2-(6)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

5w-3/w-8=0

We multiply all the terms by the denominator


5w*w-8*w-3=0

We add all the numbers together, and all the variables

-8w+5w*w-3=0

Wy multiply elements

5w^2-8w-3=0

a = 5; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·5·(-3)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{31}}{2*5}=\frac{8-2\sqrt{31}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{31}}{2*5}=\frac{8+2\sqrt{31}}{10}
$