3.05827514^(1/7)=k

Solution for 3.05827514^(1/7)=k equation:

3.05827514^(1/7)=k

We move all terms to the left:

3.05827514^(1/7)-(k)=0

We add all the numbers together, and all the variables

-k+3.05827514^(+1/7)=0

We add all the numbers together, and all the variables

-1k+3.05827514^(+1/7)=0

We multiply all the terms by the denominator


-1k*7)+3.05827514^(+1=0

Wy multiply elements

-7k^2+1=0

a = -7; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-7)·1
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-7}=\frac{0-2\sqrt{7}}{-14}
=-\frac{2\sqrt{7}}{-14}
=-\frac{\sqrt{7}}{-7}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-7}=\frac{0+2\sqrt{7}}{-14}
=\frac{2\sqrt{7}}{-14}
=\frac{\sqrt{7}}{-7}
$