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

Solution for 1/2y+5-4/4y=0 equation:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


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

We multiply all the terms by the denominator


4y+(-8y)+5*8y^2=0

Wy multiply elements

40y^2+4y+(-8y)=0

We get rid of parentheses

40y^2+4y-8y=0

We add all the numbers together, and all the variables

40y^2-4y=0

a = 40; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·40·0
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*40}=\frac{0}{80}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*40}=\frac{8}{80}
=1/10
$