7/2w+8=13/4w+10

Solution for 7/2w+8=13/4w+10 equation:

7/2w+8=13/4w+10

We move all terms to the left:

7/2w+8-(13/4w+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

7/2w-13/4w-10+8=0

We calculate fractions


28w/8w^2+(-26w)/8w^2-10+8=0

We add all the numbers together, and all the variables

28w/8w^2+(-26w)/8w^2-2=0

We multiply all the terms by the denominator


28w+(-26w)-2*8w^2=0

Wy multiply elements

-16w^2+28w+(-26w)=0

We get rid of parentheses

-16w^2+28w-26w=0

We add all the numbers together, and all the variables

-16w^2+2w=0

a = -16; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-16)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-16}=\frac{-4}{-32}
=1/8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-16}=\frac{0}{-32}
=0
$