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

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

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

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


(-64w^2)/72w^2+(-126w)/72w^2+(-108w)/72w^2+2=0

We multiply all the terms by the denominator


(-64w^2)+(-126w)+(-108w)+2*72w^2=0

Wy multiply elements

(-64w^2)+144w^2+(-126w)+(-108w)=0

We get rid of parentheses

-64w^2+144w^2-126w-108w=0

We add all the numbers together, and all the variables

80w^2-234w=0

a = 80; b = -234; c = 0;
Δ = b2-4ac
Δ = -2342-4·80·0
Δ = 54756
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{54756}=234$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-234}{2*80}=\frac{0}{160}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+234}{2*80}=\frac{468}{160}
=2+37/40
$