6x=19+20/x

Solution for 6x=19+20/x equation:

6x=19+20/x

We move all terms to the left:

6x-(19+20/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(20/x+19)=0

We get rid of parentheses

6x-20/x-19=0

We multiply all the terms by the denominator


6x*x-19*x-20=0

We add all the numbers together, and all the variables

-19x+6x*x-20=0

Wy multiply elements

6x^2-19x-20=0

a = 6; b = -19; c = -20;
Δ = b2-4ac
Δ = -192-4·6·(-20)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-29}{2*6}=\frac{-10}{12}
=-5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+29}{2*6}=\frac{48}{12}
=4
$