2/x=5x-3

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

2/x=5x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-5x+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x-5x*x+2=0

Wy multiply elements

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

a = -5; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-5)·2
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{-(3)-7}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-5}=\frac{4}{-10}
=-2/5
$