-1/3y-6y=-11

Solution for -1/3y-6y=-11 equation:

-1/3y-6y=-11

We move all terms to the left:

-1/3y-6y-(-11)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-6y-1/3y+11=0

We multiply all the terms by the denominator


-6y*3y+11*3y-1=0

Wy multiply elements

-18y^2+33y-1=0

a = -18; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·(-18)·(-1)
Δ = 1017
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:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{113}}{2*-18}=\frac{-33-3\sqrt{113}}{-36}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{113}}{2*-18}=\frac{-33+3\sqrt{113}}{-36}
$