1/5y+y=2

Solution for 1/5y+y=2 equation:

1/5y+y=2

We move all terms to the left:

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


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/5y-2=0

We multiply all the terms by the denominator


y*5y-2*5y+1=0

Wy multiply elements

5y^2-10y+1=0

a = 5; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·5·1
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{5}}{2*5}=\frac{10-4\sqrt{5}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{5}}{2*5}=\frac{10+4\sqrt{5}}{10}
$