6x^2/x=19

Solution for 6x^2/x=19 equation:

6x^2/x=19

We move all terms to the left:

6x^2/x-(19)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


6x^2-19*x=0

We add all the numbers together, and all the variables

6x^2-19x=0

a = 6; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·6·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*6}=\frac{38}{12}
=3+1/6
$