3(4^2x-1=24)

Solution for 3(4^2x-1=24) equation:

3(4^2x-1=24)

We move all terms to the left:

3(4^2x-1-(24))=0

We multiply parentheses

12x^2-3-72=0

We add all the numbers together, and all the variables

12x^2-75=0

a = 12; b = 0; c = -75;
Δ = b2-4ac
Δ = 02-4·12·(-75)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*12}=\frac{-60}{24}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*12}=\frac{60}{24}
=2+1/2
$