1/2y+5-3/5y=0

Solution for 1/2y+5-3/5y=0 equation:

1/2y+5-3/5y=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We calculate fractions


5y/10y^2+(-6y)/10y^2+5=0

We multiply all the terms by the denominator


5y+(-6y)+5*10y^2=0

Wy multiply elements

50y^2+5y+(-6y)=0

We get rid of parentheses

50y^2+5y-6y=0

We add all the numbers together, and all the variables

50y^2-1y=0

a = 50; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·50·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*50}=\frac{0}{100}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*50}=\frac{2}{100}
=1/50
$