1/3y+2.5-2.3y=1.2

Solution for 1/3y+2.5-2.3y=1.2 equation:

1/3y+2.5-2.3y=1.2

We move all terms to the left:

1/3y+2.5-2.3y-(1.2)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-2.3y+1/3y+1.3=0

We multiply all the terms by the denominator


-(2.3y)*3y+(1.3)*3y+1=0

We add all the numbers together, and all the variables

-(+2.3y)*3y+(1.3)*3y+1=0

We multiply parentheses

-6y^2+3.9y+1=0

a = -6; b = 3.9; c = +1;
Δ = b2-4ac
Δ = 3.92-4·(-6)·1
Δ = 39.21
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{-(3.9)-\sqrt{39.21}}{2*-6}=\frac{-3.9-\sqrt{39.21}}{-12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.9)+\sqrt{39.21}}{2*-6}=\frac{-3.9+\sqrt{39.21}}{-12}
$