4*3^2x-5=16

Solution for 4*3^2x-5=16 equation:

4*3^2x-5=16

We move all terms to the left:

4*3^2x-5-(16)=0

We add all the numbers together, and all the variables

4*3^2x-21=0

Wy multiply elements

12x^2-21=0

a = 12; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·12·(-21)
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*12}=\frac{0-12\sqrt{7}}{24}
=-\frac{12\sqrt{7}}{24}
=-\frac{\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*12}=\frac{0+12\sqrt{7}}{24}
=\frac{12\sqrt{7}}{24}
=\frac{\sqrt{7}}{2}
$