9/2y+90=y

Solution for 9/2y+90=y equation:

9/2y+90=y

We move all terms to the left:

9/2y+90-(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

-1y+9/2y+90=0

We multiply all the terms by the denominator


-1y*2y+90*2y+9=0

Wy multiply elements

-2y^2+180y+9=0

a = -2; b = 180; c = +9;
Δ = b2-4ac
Δ = 1802-4·(-2)·9
Δ = 32472
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:

$\sqrt{\Delta}=\sqrt{32472}=\sqrt{36*902}=\sqrt{36}*\sqrt{902}=6\sqrt{902}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{902}}{2*-2}=\frac{-180-6\sqrt{902}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{902}}{2*-2}=\frac{-180+6\sqrt{902}}{-4}
$