40/x=5x

Solution for 40/x=5x equation:

40/x=5x

We move all terms to the left:

40/x-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+40/x=0

We multiply all the terms by the denominator


-5x*x+40=0

Wy multiply elements

-5x^2+40=0

a = -5; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-5)·40
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-5}=\frac{0-20\sqrt{2}}{-10}
=-\frac{20\sqrt{2}}{-10}
=-\frac{2\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-5}=\frac{0+20\sqrt{2}}{-10}
=\frac{20\sqrt{2}}{-10}
=\frac{2\sqrt{2}}{-1}
$