10/y-2y=3

Solution for 10/y-2y=3 equation:

10/y-2y=3

We move all terms to the left:

10/y-2y-(3)=0


Domain of the equation: y!=0

y∈R


We add all the numbers together, and all the variables

-2y+10/y-3=0

We multiply all the terms by the denominator


-2y*y-3*y+10=0

We add all the numbers together, and all the variables

-3y-2y*y+10=0

Wy multiply elements

-2y^2-3y+10=0

a = -2; b = -3; c = +10;
Δ = b2-4ac
Δ = -32-4·(-2)·10
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*-2}=\frac{3-\sqrt{89}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*-2}=\frac{3+\sqrt{89}}{-4}
$