6x2/x=12/11

Solution for 6x2/x=12/11 equation:

6x^2/x=12/11

We move all terms to the left:

6x^2/x-(12/11)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x^2/x-(+12/11)=0

We get rid of parentheses

6x^2/x-12/11=0

We calculate fractions


66x^2/11x+(-12x)/11x=0

We multiply all the terms by the denominator


66x^2+(-12x)=0

We get rid of parentheses

66x^2-12x=0

a = 66; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·66·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*66}=\frac{0}{132}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*66}=\frac{24}{132}
=2/11
$