(35y-20)/(18y+99)=y

Solution for (35y-20)/(18y+99)=y equation:

(35y-20)/(18y+99)=y

We move all terms to the left:

(35y-20)/(18y+99)-(y)=0


Domain of the equation: (18y+99)!=0

We move all terms containing y to the left, all other terms to the right

18y!=-99

y!=-99/18

y!=-5+1/2

y∈R


We add all the numbers together, and all the variables

-1y+(35y-20)/(18y+99)=0

We multiply all the terms by the denominator


-1y*(18y+99)+(35y-20)=0

We multiply parentheses

-18y^2-99y+(35y-20)=0

We get rid of parentheses

-18y^2-99y+35y-20=0

We add all the numbers together, and all the variables

-18y^2-64y-20=0

a = -18; b = -64; c = -20;
Δ = b2-4ac
Δ = -642-4·(-18)·(-20)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{166}}{2*-18}=\frac{64-4\sqrt{166}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{166}}{2*-18}=\frac{64+4\sqrt{166}}{-36}
$