14/x-2=10x

Solution for 14/x-2=10x equation:

14/x-2=10x

We move all terms to the left:

14/x-2-(10x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-10x+14/x-2=0

We multiply all the terms by the denominator


-10x*x-2*x+14=0

We add all the numbers together, and all the variables

-2x-10x*x+14=0

Wy multiply elements

-10x^2-2x+14=0

a = -10; b = -2; c = +14;
Δ = b2-4ac
Δ = -22-4·(-10)·14
Δ = 564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{141}}{2*-10}=\frac{2-2\sqrt{141}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{141}}{2*-10}=\frac{2+2\sqrt{141}}{-20}
$