3/x=2x-45

Solution for 3/x=2x-45 equation:

3/x=2x-45

We move all terms to the left:

3/x-(2x-45)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

3/x-2x+45=0

We multiply all the terms by the denominator


-2x*x+45*x+3=0

We add all the numbers together, and all the variables

45x-2x*x+3=0

Wy multiply elements

-2x^2+45x+3=0

a = -2; b = 45; c = +3;
Δ = b2-4ac
Δ = 452-4·(-2)·3
Δ = 2049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{2049}}{2*-2}=\frac{-45-\sqrt{2049}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2049}}{2*-2}=\frac{-45+\sqrt{2049}}{-4}
$