w-4/5w-13=-2

Solution for w-4/5w-13=-2 equation:

w-4/5w-13=-2

We move all terms to the left:

w-4/5w-13-(-2)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R


We add all the numbers together, and all the variables

w-4/5w-11=0

We multiply all the terms by the denominator


w*5w-11*5w-4=0

Wy multiply elements

5w^2-55w-4=0

a = 5; b = -55; c = -4;
Δ = b2-4ac
Δ = -552-4·5·(-4)
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-3\sqrt{345}}{2*5}=\frac{55-3\sqrt{345}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+3\sqrt{345}}{2*5}=\frac{55+3\sqrt{345}}{10}
$