75/x=5x=15

Solution for 75/x=5x=15 equation:

75/x=5x=15

We move all terms to the left:

75/x-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+75/x=0

We multiply all the terms by the denominator


-5x*x+75=0

Wy multiply elements

-5x^2+75=0

a = -5; b = 0; c = +75;
Δ = b2-4ac
Δ = 02-4·(-5)·75
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{15}}{2*-5}=\frac{0-10\sqrt{15}}{-10}
=-\frac{10\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{15}}{2*-5}=\frac{0+10\sqrt{15}}{-10}
=\frac{10\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-1}
$