3x-8.1/x=6.4

Solution for 3x-8.1/x=6.4 equation:

3x-8.1/x=6.4

We move all terms to the left:

3x-8.1/x-(6.4)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x-8.1/x-6.4=0

We multiply all the terms by the denominator


3x*x-(6.4)*x-8.1=0

We multiply parentheses

3x*x-6.4x-8.1=0

Wy multiply elements

3x^2-6.4x-8.1=0

a = 3; b = -6.4; c = -8.1;
Δ = b2-4ac
Δ = -6.42-4·3·(-8.1)
Δ = 138.16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6.4)-\sqrt{138.16}}{2*3}=\frac{6.4-\sqrt{138.16}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.4)+\sqrt{138.16}}{2*3}=\frac{6.4+\sqrt{138.16}}{6}
$