1/4y-1/8=2/5y+5

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

1/4y-1/8=2/5y+5

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 5y+5)!=0

y∈R


We get rid of parentheses

1/4y-2/5y-5-1/8=0

We calculate fractions


(-100y^2)/1280y^2+320y/1280y^2+(-512y)/1280y^2-5=0

We multiply all the terms by the denominator


(-100y^2)+320y+(-512y)-5*1280y^2=0

Wy multiply elements

(-100y^2)-6400y^2+320y+(-512y)=0

We get rid of parentheses

-100y^2-6400y^2+320y-512y=0

We add all the numbers together, and all the variables

-6500y^2-192y=0

a = -6500; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·(-6500)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*-6500}=\frac{0}{-13000}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*-6500}=\frac{384}{-13000}
=-48/1625
$