5/16+3/8y=2+1/4y

Solution for 5/16+3/8y=2+1/4y equation:

5/16+3/8y=2+1/4y

We move all terms to the left:

5/16+3/8y-(2+1/4y)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/8y-(1/4y+2)+5/16=0

We get rid of parentheses

3/8y-1/4y-2+5/16=0

We calculate fractions


640y^2/512y^2+192y/512y^2+(-128y)/512y^2-2=0

We multiply all the terms by the denominator


640y^2+192y+(-128y)-2*512y^2=0

Wy multiply elements

640y^2-1024y^2+192y+(-128y)=0

We get rid of parentheses

640y^2-1024y^2+192y-128y=0

We add all the numbers together, and all the variables

-384y^2+64y=0

a = -384; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-384)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-384}=\frac{-128}{-768}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-384}=\frac{0}{-768}
=0
$