(18/46)^4=x

Solution for (18/46)^4=x equation:

(18/46)^4=x

We move all terms to the left:

(18/46)^4-(x)=0

We add all the numbers together, and all the variables

-x+(+18/46)^4=0

We add all the numbers together, and all the variables

-1x+(+18/46)^4=0

We multiply all the terms by the denominator


-1x*46)^4+(+18=0

Wy multiply elements

-46x^2+18=0

a = -46; b = 0; c = +18;
Δ = b2-4ac
Δ = 02-4·(-46)·18
Δ = 3312
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:

$\sqrt{\Delta}=\sqrt{3312}=\sqrt{144*23}=\sqrt{144}*\sqrt{23}=12\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{23}}{2*-46}=\frac{0-12\sqrt{23}}{-92}
=-\frac{12\sqrt{23}}{-92}
=-\frac{3\sqrt{23}}{-23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{23}}{2*-46}=\frac{0+12\sqrt{23}}{-92}
=\frac{12\sqrt{23}}{-92}
=\frac{3\sqrt{23}}{-23}
$