-1/4w-2/3=1/2w+7

Solution for -1/4w-2/3=1/2w+7 equation:

-1/4w-2/3=1/2w+7

We move all terms to the left:

-1/4w-2/3-(1/2w+7)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w+7)!=0

w∈R


We get rid of parentheses

-1/4w-1/2w-7-2/3=0

We calculate fractions


(-32w^2)/72w^2+(-18w)/72w^2+(-36w)/72w^2-7=0

We multiply all the terms by the denominator


(-32w^2)+(-18w)+(-36w)-7*72w^2=0

Wy multiply elements

(-32w^2)-504w^2+(-18w)+(-36w)=0

We get rid of parentheses

-32w^2-504w^2-18w-36w=0

We add all the numbers together, and all the variables

-536w^2-54w=0

a = -536; b = -54; c = 0;
Δ = b2-4ac
Δ = -542-4·(-536)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-54}{2*-536}=\frac{0}{-1072}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+54}{2*-536}=\frac{108}{-1072}
=-27/268
$