(3x)2-10^4=56

Solution for (3x)2-10^4=56 equation:

(3x)2-10^4=56

We move all terms to the left:

(3x)2-10^4-(56)=0

determiningTheFunctionDomain
3x2-56-10^4=0

We add all the numbers together, and all the variables

3x^2-10056=0

a = 3; b = 0; c = -10056;
Δ = b2-4ac
Δ = 02-4·3·(-10056)
Δ = 120672
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:

$\sqrt{\Delta}=\sqrt{120672}=\sqrt{144*838}=\sqrt{144}*\sqrt{838}=12\sqrt{838}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{838}}{2*3}=\frac{0-12\sqrt{838}}{6}
=-\frac{12\sqrt{838}}{6}
=-2\sqrt{838}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{838}}{2*3}=\frac{0+12\sqrt{838}}{6}
=\frac{12\sqrt{838}}{6}
=2\sqrt{838}
$