12/x+19=5x-9

Solution for 12/x+19=5x-9 equation:

12/x+19=5x-9

We move all terms to the left:

12/x+19-(5x-9)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

12/x-5x+9+19=0

We multiply all the terms by the denominator


-5x*x+9*x+19*x+12=0

We add all the numbers together, and all the variables

28x-5x*x+12=0

Wy multiply elements

-5x^2+28x+12=0

a = -5; b = 28; c = +12;
Δ = b2-4ac
Δ = 282-4·(-5)·12
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-32}{2*-5}=\frac{-60}{-10}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+32}{2*-5}=\frac{4}{-10}
=-2/5
$