3y=11/2y-10

Solution for 3y=11/2y-10 equation:

3y=11/2y-10

We move all terms to the left:

3y-(11/2y-10)=0


Domain of the equation: 2y-10)!=0

y∈R


We get rid of parentheses

3y-11/2y+10=0

We multiply all the terms by the denominator


3y*2y+10*2y-11=0

Wy multiply elements

6y^2+20y-11=0

a = 6; b = 20; c = -11;
Δ = b2-4ac
Δ = 202-4·6·(-11)
Δ = 664
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:

$\sqrt{\Delta}=\sqrt{664}=\sqrt{4*166}=\sqrt{4}*\sqrt{166}=2\sqrt{166}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{166}}{2*6}=\frac{-20-2\sqrt{166}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{166}}{2*6}=\frac{-20+2\sqrt{166}}{12}
$