31/2w+8=31/4w+10

Solution for 31/2w+8=31/4w+10 equation:

31/2w+8=31/4w+10

We move all terms to the left:

31/2w+8-(31/4w+10)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w+10)!=0

w∈R


We get rid of parentheses

31/2w-31/4w-10+8=0

We calculate fractions


124w/8w^2+(-62w)/8w^2-10+8=0

We add all the numbers together, and all the variables

124w/8w^2+(-62w)/8w^2-2=0

We multiply all the terms by the denominator


124w+(-62w)-2*8w^2=0

Wy multiply elements

-16w^2+124w+(-62w)=0

We get rid of parentheses

-16w^2+124w-62w=0

We add all the numbers together, and all the variables

-16w^2+62w=0

a = -16; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-16)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-16}=\frac{-124}{-32}
=3+7/8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-16}=\frac{0}{-32}
=0
$