1,5y+2,5=1/3y-1

Solution for 1,5y+2,5=1/3y-1 equation:

1.5y+2.5=1/3y-1

We move all terms to the left:

1.5y+2.5-(1/3y-1)=0


Domain of the equation: 3y-1)!=0

y∈R


We get rid of parentheses

1.5y-1/3y+1+2.5=0

We multiply all the terms by the denominator


(1.5y)*3y+1*3y+(2.5)*3y-1=0

We add all the numbers together, and all the variables

(+1.5y)*3y+1*3y+(2.5)*3y-1=0

We multiply parentheses

3y^2+1*3y+7.5y-1=0

Wy multiply elements

3y^2+3y+7.5y-1=0

We add all the numbers together, and all the variables

3y^2+10.5y-1=0

a = 3; b = 10.5; c = -1;
Δ = b2-4ac
Δ = 10.52-4·3·(-1)
Δ = 122.25
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{-(10.5)-\sqrt{122.25}}{2*3}=\frac{-10.5-\sqrt{122.25}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10.5)+\sqrt{122.25}}{2*3}=\frac{-10.5+\sqrt{122.25}}{6}
$