25/x=2x

Solution for 25/x=2x equation:

25/x=2x

We move all terms to the left:

25/x-(2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+25/x=0

We multiply all the terms by the denominator


-2x*x+25=0

Wy multiply elements

-2x^2+25=0

a = -2; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-2)·25
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*-2}=\frac{0-10\sqrt{2}}{-4}
=-\frac{10\sqrt{2}}{-4}
=-\frac{5\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-2}=\frac{0+10\sqrt{2}}{-4}
=\frac{10\sqrt{2}}{-4}
=\frac{5\sqrt{2}}{-2}
$