17a=54/a

Solution for 17a=54/a equation:

17a=54/a

We move all terms to the left:

17a-(54/a)=0


Domain of the equation: a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

17a-(+54/a)=0

We get rid of parentheses

17a-54/a=0

We multiply all the terms by the denominator


17a*a-54=0

Wy multiply elements

17a^2-54=0

a = 17; b = 0; c = -54;
Δ = b2-4ac
Δ = 02-4·17·(-54)
Δ = 3672
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3672}=\sqrt{36*102}=\sqrt{36}*\sqrt{102}=6\sqrt{102}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{102}}{2*17}=\frac{0-6\sqrt{102}}{34}
=-\frac{6\sqrt{102}}{34}
=-\frac{3\sqrt{102}}{17}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{102}}{2*17}=\frac{0+6\sqrt{102}}{34}
=\frac{6\sqrt{102}}{34}
=\frac{3\sqrt{102}}{17}
$