3w-22=2/5w-11

Solution for 3w-22=2/5w-11 equation:

3w-22=2/5w-11

We move all terms to the left:

3w-22-(2/5w-11)=0


Domain of the equation: 5w-11)!=0

w∈R


We get rid of parentheses

3w-2/5w+11-22=0

We multiply all the terms by the denominator


3w*5w+11*5w-22*5w-2=0

Wy multiply elements

15w^2+55w-110w-2=0

We add all the numbers together, and all the variables

15w^2-55w-2=0

a = 15; b = -55; c = -2;
Δ = b2-4ac
Δ = -552-4·15·(-2)
Δ = 3145
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{-(-55)-\sqrt{3145}}{2*15}=\frac{55-\sqrt{3145}}{30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{3145}}{2*15}=\frac{55+\sqrt{3145}}{30}
$