811/17y+12=2y-6

Solution for 811/17y+12=2y-6 equation:

811/17y+12=2y-6

We move all terms to the left:

811/17y+12-(2y-6)=0


Domain of the equation: 17y!=0

y!=0/17

y!=0

y∈R


We get rid of parentheses

811/17y-2y+6+12=0

We multiply all the terms by the denominator


-2y*17y+6*17y+12*17y+811=0

Wy multiply elements

-34y^2+102y+204y+811=0

We add all the numbers together, and all the variables

-34y^2+306y+811=0

a = -34; b = 306; c = +811;
Δ = b2-4ac
Δ = 3062-4·(-34)·811
Δ = 203932
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:

$\sqrt{\Delta}=\sqrt{203932}=\sqrt{4*50983}=\sqrt{4}*\sqrt{50983}=2\sqrt{50983}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(306)-2\sqrt{50983}}{2*-34}=\frac{-306-2\sqrt{50983}}{-68}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(306)+2\sqrt{50983}}{2*-34}=\frac{-306+2\sqrt{50983}}{-68}
$