2w+6/w-3=5

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

2w+6/w-3=5

We move all terms to the left:

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


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

2w+6/w-8=0

We multiply all the terms by the denominator


2w*w-8*w+6=0

We add all the numbers together, and all the variables

-8w+2w*w+6=0

Wy multiply elements

2w^2-8w+6=0

a = 2; b = -8; c = +6;
Δ = b2-4ac
Δ = -82-4·2·6
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*2}=\frac{4}{4}
=1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*2}=\frac{12}{4}
=3
$