28-2.2y=11/6y+262.6

Solution for 28-2.2y=11/6y+262.6 equation:

28-2.2y=11/6y+262.6

We move all terms to the left:

28-2.2y-(11/6y+262.6)=0


Domain of the equation: 6y+262.6)!=0

y∈R


We get rid of parentheses

-2.2y-11/6y-262.6+28=0

We multiply all the terms by the denominator


-(2.2y)*6y-(262.6)*6y+28*6y-11=0

We add all the numbers together, and all the variables

-(+2.2y)*6y-(262.6)*6y+28*6y-11=0

We multiply parentheses

-12y^2-1575.6y+28*6y-11=0

Wy multiply elements

-12y^2-1575.6y+168y-11=0

We add all the numbers together, and all the variables

-12y^2-1407.6y-11=0

a = -12; b = -1407.6; c = -11;
Δ = b2-4ac
Δ = -1407.62-4·(-12)·(-11)
Δ = 1980809.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1407.6)-\sqrt{1980809.76}}{2*-12}=\frac{1407.6-\sqrt{1980809.76}}{-24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1407.6)+\sqrt{1980809.76}}{2*-12}=\frac{1407.6+\sqrt{1980809.76}}{-24}
$