162^(3/4)=2x

Solution for 162^(3/4)=2x equation:

162^(3/4)=2x

We move all terms to the left:

162^(3/4)-(2x)=0

We add all the numbers together, and all the variables

-2x+162^(+3/4)=0

We multiply all the terms by the denominator


-2x*4)+162^(+3=0

Wy multiply elements

-8x^2+3=0

a = -8; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-8)·3
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*-8}=\frac{0-4\sqrt{6}}{-16}
=-\frac{4\sqrt{6}}{-16}
=-\frac{\sqrt{6}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*-8}=\frac{0+4\sqrt{6}}{-16}
=\frac{4\sqrt{6}}{-16}
=\frac{\sqrt{6}}{-4}
$