3/x+5=2x

Solution for 3/x+5=2x equation:

3/x+5=2x

We move all terms to the left:

3/x+5-(2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+3/x+5=0

We multiply all the terms by the denominator


-2x*x+5*x+3=0

We add all the numbers together, and all the variables

5x-2x*x+3=0

Wy multiply elements

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

a = -2; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-2)·3
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*-2}=\frac{2}{-4}
=-1/2
$