40=44-3/2y+y

Solution for 40=44-3/2y+y equation:

40=44-3/2y+y

We move all terms to the left:

40-(44-3/2y+y)=0


Domain of the equation: 2y+y)!=0

y∈R


We add all the numbers together, and all the variables

-(y-3/2y+44)+40=0

We get rid of parentheses

-y+3/2y-44+40=0

We multiply all the terms by the denominator


-y*2y-44*2y+40*2y+3=0

Wy multiply elements

-2y^2-88y+80y+3=0

We add all the numbers together, and all the variables

-2y^2-8y+3=0

a = -2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-2)·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{22}}{2*-2}=\frac{8-2\sqrt{22}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{22}}{2*-2}=\frac{8+2\sqrt{22}}{-4}
$