5y*0.2=1*1/3*y-0.9

Solution for 5y*0.2=1*1/3*y-0.9 equation:

5y*0.2=1*1/3y-0.9

We move all terms to the left:

5y*0.2-(1*1/3y-0.9)=0


Domain of the equation: 3y-0.9)!=0

y∈R


Wy multiply elements

y-(1*1/3y-0.9)=0

We get rid of parentheses

y-1*1/3y+0.9=0

We multiply all the terms by the denominator


y*3y+(0.9)*3y-1*1=0

We add all the numbers together, and all the variables

y*3y+(0.9)*3y-1=0

We multiply parentheses

y*3y+2.7y-1=0

Wy multiply elements

3y^2+2.7y-1=0

a = 3; b = 2.7; c = -1;
Δ = b2-4ac
Δ = 2.72-4·3·(-1)
Δ = 19.29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.7)-\sqrt{19.29}}{2*3}=\frac{-2.7-\sqrt{19.29}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.7)+\sqrt{19.29}}{2*3}=\frac{-2.7+\sqrt{19.29}}{6}
$