-7/2w-5/4=1/3w-3

Solution for -7/2w-5/4=1/3w-3 equation:

-7/2w-5/4=1/3w-3

We move all terms to the left:

-7/2w-5/4-(1/3w-3)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



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

w∈R


We get rid of parentheses

-7/2w-1/3w+3-5/4=0

We calculate fractions


(-90w^2)/96w^2+(-336w)/96w^2+(-32w)/96w^2+3=0

We multiply all the terms by the denominator


(-90w^2)+(-336w)+(-32w)+3*96w^2=0

Wy multiply elements

(-90w^2)+288w^2+(-336w)+(-32w)=0

We get rid of parentheses

-90w^2+288w^2-336w-32w=0

We add all the numbers together, and all the variables

198w^2-368w=0

a = 198; b = -368; c = 0;
Δ = b2-4ac
Δ = -3682-4·198·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-368}{2*198}=\frac{0}{396}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+368}{2*198}=\frac{736}{396}
=1+85/99
$