3/2y+2.3-1/2y=4.3+y

Solution for 3/2y+2.3-1/2y=4.3+y equation:

3/2y+2.3-1/2y=4.3+y

We move all terms to the left:

3/2y+2.3-1/2y-(4.3+y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3/2y-1/2y-(y+4.3)+2.3=0

We get rid of parentheses

3/2y-1/2y-y-4.3+2.3=0

We multiply all the terms by the denominator


-y*2y-(4.3)*2y+(2.3)*2y+3-1=0

We add all the numbers together, and all the variables

-y*2y-(4.3)*2y+(2.3)*2y+2=0

We multiply parentheses

-y*2y-8.6y+4.6y+2=0

Wy multiply elements

-2y^2-8.6y+4.6y+2=0

We add all the numbers together, and all the variables

-2y^2-4y+2=0

a = -2; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-2)·2
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{2}}{2*-2}=\frac{4-4\sqrt{2}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{2}}{2*-2}=\frac{4+4\sqrt{2}}{-4}
$