8w+1=-2/3w-8

Solution for 8w+1=-2/3w-8 equation:

8w+1=-2/3w-8

We move all terms to the left:

8w+1-(-2/3w-8)=0


Domain of the equation: 3w-8)!=0

w∈R


We get rid of parentheses

8w+2/3w+8+1=0

We multiply all the terms by the denominator


8w*3w+8*3w+1*3w+2=0

Wy multiply elements

24w^2+24w+3w+2=0

We add all the numbers together, and all the variables

24w^2+27w+2=0

a = 24; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·24·2
Δ = 537
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{-(27)-\sqrt{537}}{2*24}=\frac{-27-\sqrt{537}}{48}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{537}}{2*24}=\frac{-27+\sqrt{537}}{48}
$