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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 5w+2)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-150w^2)/160w^2+80w/160w^2+(-64w)/160w^2-2=0

We multiply all the terms by the denominator


(-150w^2)+80w+(-64w)-2*160w^2=0

Wy multiply elements

(-150w^2)-320w^2+80w+(-64w)=0

We get rid of parentheses

-150w^2-320w^2+80w-64w=0

We add all the numbers together, and all the variables

-470w^2+16w=0

a = -470; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-470)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-470}=\frac{-32}{-940}
=8/235
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-470}=\frac{0}{-940}
=0
$