1275/x=5x

Solution for 1275/x=5x equation:

1275/x=5x

We move all terms to the left:

1275/x-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+1275/x=0

We multiply all the terms by the denominator


-5x*x+1275=0

Wy multiply elements

-5x^2+1275=0

a = -5; b = 0; c = +1275;
Δ = b2-4ac
Δ = 02-4·(-5)·1275
Δ = 25500
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:

$\sqrt{\Delta}=\sqrt{25500}=\sqrt{100*255}=\sqrt{100}*\sqrt{255}=10\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{255}}{2*-5}=\frac{0-10\sqrt{255}}{-10}
=-\frac{10\sqrt{255}}{-10}
=-\frac{\sqrt{255}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{255}}{2*-5}=\frac{0+10\sqrt{255}}{-10}
=\frac{10\sqrt{255}}{-10}
=\frac{\sqrt{255}}{-1}
$