5-1/2y=5/8y+2

Solution for 5-1/2y=5/8y+2 equation:

5-1/2y=5/8y+2

We move all terms to the left:

5-1/2y-(5/8y+2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 8y+2)!=0

y∈R


We get rid of parentheses

-1/2y-5/8y-2+5=0

We calculate fractions


(-8y)/16y^2+(-10y)/16y^2-2+5=0

We add all the numbers together, and all the variables

(-8y)/16y^2+(-10y)/16y^2+3=0

We multiply all the terms by the denominator


(-8y)+(-10y)+3*16y^2=0

Wy multiply elements

48y^2+(-8y)+(-10y)=0

We get rid of parentheses

48y^2-8y-10y=0

We add all the numbers together, and all the variables

48y^2-18y=0

a = 48; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·48·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*48}=\frac{0}{96}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*48}=\frac{36}{96}
=3/8
$