-1/3w-8=-5w-22

Solution for -1/3w-8=-5w-22 equation:

-1/3w-8=-5w-22

We move all terms to the left:

-1/3w-8-(-5w-22)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We get rid of parentheses

-1/3w+5w+22-8=0

We multiply all the terms by the denominator


5w*3w+22*3w-8*3w-1=0

Wy multiply elements

15w^2+66w-24w-1=0

We add all the numbers together, and all the variables

15w^2+42w-1=0

a = 15; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·15·(-1)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{114}}{2*15}=\frac{-42-4\sqrt{114}}{30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{114}}{2*15}=\frac{-42+4\sqrt{114}}{30}
$