3w-3=1/7w+2

Solution for 3w-3=1/7w+2 equation:

3w-3=1/7w+2

We move all terms to the left:

3w-3-(1/7w+2)=0


Domain of the equation: 7w+2)!=0

w∈R


We get rid of parentheses

3w-1/7w-2-3=0

We multiply all the terms by the denominator


3w*7w-2*7w-3*7w-1=0

Wy multiply elements

21w^2-14w-21w-1=0

We add all the numbers together, and all the variables

21w^2-35w-1=0

a = 21; b = -35; c = -1;
Δ = b2-4ac
Δ = -352-4·21·(-1)
Δ = 1309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1309}}{2*21}=\frac{35-\sqrt{1309}}{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1309}}{2*21}=\frac{35+\sqrt{1309}}{42}
$