2/3y-8=11y=

Solution for 2/3y-8=11y= equation:

2/3y-8=11y=

We move all terms to the left:

2/3y-8-(11y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

-11y+2/3y-8=0

We multiply all the terms by the denominator


-11y*3y-8*3y+2=0

Wy multiply elements

-33y^2-24y+2=0

a = -33; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-33)·2
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{210}}{2*-33}=\frac{24-2\sqrt{210}}{-66}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{210}}{2*-33}=\frac{24+2\sqrt{210}}{-66}
$