5/2y=10+2y

Solution for 5/2y=10+2y equation:

5/2y=10+2y

We move all terms to the left:

5/2y-(10+2y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

5/2y-(2y+10)=0

We get rid of parentheses

5/2y-2y-10=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4y^2-20y+5=0

a = -4; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·(-4)·5
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*-4}=\frac{20-4\sqrt{30}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*-4}=\frac{20+4\sqrt{30}}{-8}
$