Y/2y-9=3+8y

Solution for Y/2y-9=3+8y equation:

/2Y-9=3+8Y

We move all terms to the left:

/2Y-9-(3+8Y)=0


Domain of the equation: 2Y!=0

Y!=0/2

Y!=0

Y∈R


We add all the numbers together, and all the variables

/2Y-(8Y+3)-9=0

We get rid of parentheses

/2Y-8Y-3-9=0

We multiply all the terms by the denominator


-8Y*2Y-3*2Y-9*2Y+=0

We add all the numbers together, and all the variables

-8Y*2Y-3*2Y-9*2Y=0

Wy multiply elements

-16Y^2-6Y-18Y=0

We add all the numbers together, and all the variables

-16Y^2-24Y=0

a = -16; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·(-16)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*-16}=\frac{0}{-32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*-16}=\frac{48}{-32}
=-1+1/2
$