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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


24y/32y^2+4y/32y^2-2+16=0

We add all the numbers together, and all the variables

24y/32y^2+4y/32y^2+14=0

We multiply all the terms by the denominator


24y+4y+14*32y^2=0

We add all the numbers together, and all the variables

28y+14*32y^2=0

Wy multiply elements

448y^2+28y=0

a = 448; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·448·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*448}=\frac{-56}{896}
=-1/16
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*448}=\frac{0}{896}
=0
$