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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w-3)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


16w/24w^2+21w/24w^2+(-3w)/24w^2+3=0

We multiply all the terms by the denominator


16w+21w+(-3w)+3*24w^2=0

We add all the numbers together, and all the variables

37w+(-3w)+3*24w^2=0

Wy multiply elements

72w^2+37w+(-3w)=0

We get rid of parentheses

72w^2+37w-3w=0

We add all the numbers together, and all the variables

72w^2+34w=0

a = 72; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·72·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*72}=\frac{-68}{144}
=-17/36
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*72}=\frac{0}{144}
=0
$