1/4w-3/4=1/3w+6

Solution for 1/4w-3/4=1/3w+6 equation:

1/4w-3/4=1/3w+6

We move all terms to the left:

1/4w-3/4-(1/3w+6)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 3w+6)!=0

w∈R


We get rid of parentheses

1/4w-1/3w-6-3/4=0

We calculate fractions


3w/192w^2+(-64w)/192w^2+(-9w)/192w^2-6=0

We multiply all the terms by the denominator


3w+(-64w)+(-9w)-6*192w^2=0

Wy multiply elements

-1152w^2+3w+(-64w)+(-9w)=0

We get rid of parentheses

-1152w^2+3w-64w-9w=0

We add all the numbers together, and all the variables

-1152w^2-70w=0

a = -1152; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-1152)·0
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-1152}=\frac{0}{-2304}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-1152}=\frac{140}{-2304}
=-35/576
$