3x=50/x-19

Solution for 3x=50/x-19 equation:

3x=50/x-19

We move all terms to the left:

3x-(50/x-19)=0


Domain of the equation: x-19)!=0

x∈R


We get rid of parentheses

3x-50/x+19=0

We multiply all the terms by the denominator


3x*x+19*x-50=0

We add all the numbers together, and all the variables

19x+3x*x-50=0

Wy multiply elements

3x^2+19x-50=0

a = 3; b = 19; c = -50;
Δ = b2-4ac
Δ = 192-4·3·(-50)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-31}{2*3}=\frac{-50}{6}
=-8+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+31}{2*3}=\frac{12}{6}
=2
$