11/2y=2y-10

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

11/2y=2y-10

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

11/2y-2y+10=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4y^2+20y+11=0

a = -4; b = 20; c = +11;
Δ = b2-4ac
Δ = 202-4·(-4)·11
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-24}{2*-4}=\frac{-44}{-8}
=5+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+24}{2*-4}=\frac{4}{-8}
=-1/2
$