3(4x)^2+48=49200

Solution for 3(4x)^2+48=49200 equation:

3(4x)^2+48=49200

We move all terms to the left:

3(4x)^2+48-(49200)=0

We add all the numbers together, and all the variables

34x^2-49152=0

a = 34; b = 0; c = -49152;
Δ = b2-4ac
Δ = 02-4·34·(-49152)
Δ = 6684672
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:

$\sqrt{\Delta}=\sqrt{6684672}=\sqrt{65536*102}=\sqrt{65536}*\sqrt{102}=256\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-256\sqrt{102}}{2*34}=\frac{0-256\sqrt{102}}{68}
=-\frac{256\sqrt{102}}{68}
=-\frac{64\sqrt{102}}{17}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+256\sqrt{102}}{2*34}=\frac{0+256\sqrt{102}}{68}
=\frac{256\sqrt{102}}{68}
=\frac{64\sqrt{102}}{17}
$