5y*0.2=4/3*y-0.9

Solution for 5y*0.2=4/3*y-0.9 equation:

5y*0.2=4/3y-0.9

We move all terms to the left:

5y*0.2-(4/3y-0.9)=0


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

y∈R


Wy multiply elements

y-(4/3y-0.9)=0

We get rid of parentheses

y-4/3y+0.9=0

We multiply all the terms by the denominator


y*3y+(0.9)*3y-4=0

We multiply parentheses

y*3y+2.7y-4=0

Wy multiply elements

3y^2+2.7y-4=0

a = 3; b = 2.7; c = -4;
Δ = b2-4ac
Δ = 2.72-4·3·(-4)
Δ = 55.29
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{55.29}}{2*3}=\frac{-2.7-\sqrt{55.29}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.7)+\sqrt{55.29}}{2*3}=\frac{-2.7+\sqrt{55.29}}{6}
$