2y-4/10y+2=0.6

Solution for 2y-4/10y+2=0.6 equation:

2y-4/10y+2=0.6

We move all terms to the left:

2y-4/10y+2-(0.6)=0


Domain of the equation: 10y!=0

y!=0/10

y!=0

y∈R


We add all the numbers together, and all the variables

2y-4/10y+1.4=0

We multiply all the terms by the denominator


2y*10y+(1.4)*10y-4=0

We multiply parentheses

2y*10y+14y-4=0

Wy multiply elements

20y^2+14y-4=0

a = 20; b = 14; c = -4;
Δ = b2-4ac
Δ = 142-4·20·(-4)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{129}}{2*20}=\frac{-14-2\sqrt{129}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{129}}{2*20}=\frac{-14+2\sqrt{129}}{40}
$