5/x=175x

Solution for 5/x=175x equation:

5/x=175x

We move all terms to the left:

5/x-(175x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-175x+5/x=0

We multiply all the terms by the denominator


-175x*x+5=0

Wy multiply elements

-175x^2+5=0

a = -175; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-175)·5
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{35}}{2*-175}=\frac{0-10\sqrt{35}}{-350}
=-\frac{10\sqrt{35}}{-350}
=-\frac{\sqrt{35}}{-35}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{35}}{2*-175}=\frac{0+10\sqrt{35}}{-350}
=\frac{10\sqrt{35}}{-350}
=\frac{\sqrt{35}}{-35}
$