Y=10x/x^2+1

Solution for Y=10x/x^2+1 equation:

=10Y/Y^2+1

We move all terms to the left:

-(10Y/Y^2+1)=0


Domain of the equation: Y^2+1)!=0

Y∈R


We get rid of parentheses

-10Y/Y^2-1=0

We multiply all the terms by the denominator


-10Y-1*Y^2=0

We add all the numbers together, and all the variables

-1Y^2-10Y=0

a = -1; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1}=\frac{0}{-2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1}=\frac{20}{-2}
=-10
$