1/4y-16=3/8y+64

Solution for 1/4y-16=3/8y+64 equation:

1/4y-16=3/8y+64

We move all terms to the left:

1/4y-16-(3/8y+64)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 8y+64)!=0

y∈R


We get rid of parentheses

1/4y-3/8y-64-16=0

We calculate fractions


8y/32y^2+(-12y)/32y^2-64-16=0

We add all the numbers together, and all the variables

8y/32y^2+(-12y)/32y^2-80=0

We multiply all the terms by the denominator


8y+(-12y)-80*32y^2=0

Wy multiply elements

-2560y^2+8y+(-12y)=0

We get rid of parentheses

-2560y^2+8y-12y=0

We add all the numbers together, and all the variables

-2560y^2-4y=0

a = -2560; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-2560)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-2560}=\frac{0}{-5120}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-2560}=\frac{8}{-5120}
=-1/640
$