x=(5^9)/6x

Solution for x=(5^9)/6x equation:

x=(5^9)/6x

We move all terms to the left:

x-((5^9)/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

x-5^9/6x=0

We multiply all the terms by the denominator


x*6x-5^9=0

We add all the numbers together, and all the variables

x*6x-1953125=0

Wy multiply elements

6x^2-1953125=0

a = 6; b = 0; c = -1953125;
Δ = b2-4ac
Δ = 02-4·6·(-1953125)
Δ = 46875000
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:

$\sqrt{\Delta}=\sqrt{46875000}=\sqrt{1562500*30}=\sqrt{1562500}*\sqrt{30}=1250\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1250\sqrt{30}}{2*6}=\frac{0-1250\sqrt{30}}{12}
=-\frac{1250\sqrt{30}}{12}
=-\frac{625\sqrt{30}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1250\sqrt{30}}{2*6}=\frac{0+1250\sqrt{30}}{12}
=\frac{1250\sqrt{30}}{12}
=\frac{625\sqrt{30}}{6}
$