3/5xX21=x

Solution for 3/5xX21=x equation:

3/5xx21=x

We move all terms to the left:

3/5xx21-(x)=0


Domain of the equation: 5xx21!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/5xx21=0

We multiply all the terms by the denominator


-1x*5xx21+3=0

Wy multiply elements

-5x^2+3=0

a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-5}
$