5/2y-y=y+5

Solution for 5/2y-y=y+5 equation:

5/2y-y=y+5

We move all terms to the left:

5/2y-y-(y+5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+5/2y-(y+5)=0

We get rid of parentheses

-1y+5/2y-y-5=0

We multiply all the terms by the denominator


-1y*2y-y*2y-5*2y+5=0

Wy multiply elements

-2y^2-2y^2-10y+5=0

We add all the numbers together, and all the variables

-4y^2-10y+5=0

a = -4; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·(-4)·5
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{5}}{2*-4}=\frac{10-6\sqrt{5}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{5}}{2*-4}=\frac{10+6\sqrt{5}}{-8}
$