9/x+3=5x=

Solution for 9/x+3=5x= equation:

9/x+3=5x=

We move all terms to the left:

9/x+3-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+9/x+3=0

We multiply all the terms by the denominator


-5x*x+3*x+9=0

We add all the numbers together, and all the variables

3x-5x*x+9=0

Wy multiply elements

-5x^2+3x+9=0

a = -5; b = 3; c = +9;
Δ = b2-4ac
Δ = 32-4·(-5)·9
Δ = 189
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{21}}{2*-5}=\frac{-3-3\sqrt{21}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{21}}{2*-5}=\frac{-3+3\sqrt{21}}{-10}
$