(9-y)-1/2y=-3

Solution for (9-y)-1/2y=-3 equation:

(9-y)-1/2y=-3

We move all terms to the left:

(9-y)-1/2y-(-3)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

(-1y+9)-1/2y-(-3)=0

We add all the numbers together, and all the variables

(-1y+9)-1/2y+3=0

We get rid of parentheses

-1y-1/2y+9+3=0

We multiply all the terms by the denominator


-1y*2y+9*2y+3*2y-1=0

Wy multiply elements

-2y^2+18y+6y-1=0

We add all the numbers together, and all the variables

-2y^2+24y-1=0

a = -2; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-2)·(-1)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{142}}{2*-2}=\frac{-24-2\sqrt{142}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{142}}{2*-2}=\frac{-24+2\sqrt{142}}{-4}
$