2/5y=2.3+3.2y

Solution for 2/5y=2.3+3.2y equation:

2/5y=2.3+3.2y

We move all terms to the left:

2/5y-(2.3+3.2y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-(3.2y+2.3)=0

We get rid of parentheses

2/5y-3.2y-2.3=0

We multiply all the terms by the denominator


-(3.2y)*5y-(2.3)*5y+2=0

We add all the numbers together, and all the variables

-(+3.2y)*5y-(2.3)*5y+2=0

We multiply parentheses

-15y^2-11.5y+2=0

a = -15; b = -11.5; c = +2;
Δ = b2-4ac
Δ = -11.52-4·(-15)·2
Δ = 252.25
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{-(-11.5)-\sqrt{252.25}}{2*-15}=\frac{11.5-\sqrt{252.25}}{-30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.5)+\sqrt{252.25}}{2*-15}=\frac{11.5+\sqrt{252.25}}{-30}
$