-2y-20=10/8y

Solution for -2y-20=10/8y equation:

-2y-20=10/8y

We move all terms to the left:

-2y-20-(10/8y)=0


Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-2y-(+10/8y)-20=0

We get rid of parentheses

-2y-10/8y-20=0

We multiply all the terms by the denominator


-2y*8y-20*8y-10=0

Wy multiply elements

-16y^2-160y-10=0

a = -16; b = -160; c = -10;
Δ = b2-4ac
Δ = -1602-4·(-16)·(-10)
Δ = 24960
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:

$\sqrt{\Delta}=\sqrt{24960}=\sqrt{64*390}=\sqrt{64}*\sqrt{390}=8\sqrt{390}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-8\sqrt{390}}{2*-16}=\frac{160-8\sqrt{390}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+8\sqrt{390}}{2*-16}=\frac{160+8\sqrt{390}}{-32}
$