3/4w+8=1/3w-77

Solution for 3/4w+8=1/3w-77 equation:

3/4w+8=1/3w-77

We move all terms to the left:

3/4w+8-(1/3w-77)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w-77)!=0

w∈R


We get rid of parentheses

3/4w-1/3w+77+8=0

We calculate fractions


9w/12w^2+(-4w)/12w^2+77+8=0

We add all the numbers together, and all the variables

9w/12w^2+(-4w)/12w^2+85=0

We multiply all the terms by the denominator


9w+(-4w)+85*12w^2=0

Wy multiply elements

1020w^2+9w+(-4w)=0

We get rid of parentheses

1020w^2+9w-4w=0

We add all the numbers together, and all the variables

1020w^2+5w=0

a = 1020; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1020·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*1020}=\frac{-10}{2040}
=-1/204
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1020}=\frac{0}{2040}
=0
$