17a=41/a=3

Solution for 17a=41/a=3 equation:

17a=41/a=3

We move all terms to the left:

17a-(41/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-(+41/a)=0

We get rid of parentheses

17a-41/a=0

We multiply all the terms by the denominator


17a*a-41=0

Wy multiply elements

17a^2-41=0

a = 17; b = 0; c = -41;
Δ = b2-4ac
Δ = 02-4·17·(-41)
Δ = 2788
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:

$\sqrt{\Delta}=\sqrt{2788}=\sqrt{4*697}=\sqrt{4}*\sqrt{697}=2\sqrt{697}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{697}}{2*17}=\frac{0-2\sqrt{697}}{34}
=-\frac{2\sqrt{697}}{34}
=-\frac{\sqrt{697}}{17}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{697}}{2*17}=\frac{0+2\sqrt{697}}{34}
=\frac{2\sqrt{697}}{34}
=\frac{\sqrt{697}}{17}
$