10+3x/x^2=1

Solution for 10+3x/x^2=1 equation:

10+3x/x^2=1

We move all terms to the left:

10+3x/x^2-(1)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

3x/x^2+9=0

We multiply all the terms by the denominator


3x+9*x^2=0

We add all the numbers together, and all the variables

9x^2+3x=0

a = 9; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·9·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*9}=\frac{-6}{18}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*9}=\frac{0}{18}
=0
$