8/x-3=2x

Solution for 8/x-3=2x equation:

8/x-3=2x

We move all terms to the left:

8/x-3-(2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+8/x-3=0

We multiply all the terms by the denominator


-2x*x-3*x+8=0

We add all the numbers together, and all the variables

-3x-2x*x+8=0

Wy multiply elements

-2x^2-3x+8=0

a = -2; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-2)·8
Δ = 73
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{-(-3)-\sqrt{73}}{2*-2}=\frac{3-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{73}}{2*-2}=\frac{3+\sqrt{73}}{-4}
$