8/x-3x=10

Solution for 8/x-3x=10 equation:

8/x-3x=10

We move all terms to the left:

8/x-3x-(10)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+8/x-10=0

We multiply all the terms by the denominator


-3x*x-10*x+8=0

We add all the numbers together, and all the variables

-10x-3x*x+8=0

Wy multiply elements

-3x^2-10x+8=0

a = -3; b = -10; c = +8;
Δ = b2-4ac
Δ = -102-4·(-3)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-3}=\frac{-4}{-6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-3}=\frac{24}{-6}
=-4
$