1/2y=y+10

Solution for 1/2y=y+10 equation:

1/2y=y+10

We move all terms to the left:

1/2y-(y+10)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-y-10=0

We multiply all the terms by the denominator


-y*2y-10*2y+1=0

Wy multiply elements

-2y^2-20y+1=0

a = -2; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-2)·1
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{102}}{2*-2}=\frac{20-2\sqrt{102}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{102}}{2*-2}=\frac{20+2\sqrt{102}}{-4}
$