12(x^2)=10^4

Solution for 12(x^2)=10^4 equation:

12(x^2)=10^4

We move all terms to the left:

12(x^2)-(10^4)=0

We add all the numbers together, and all the variables

12x^2-10000=0

a = 12; b = 0; c = -10000;
Δ = b2-4ac
Δ = 02-4·12·(-10000)
Δ = 480000
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:

$\sqrt{\Delta}=\sqrt{480000}=\sqrt{160000*3}=\sqrt{160000}*\sqrt{3}=400\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{3}}{2*12}=\frac{0-400\sqrt{3}}{24}
=-\frac{400\sqrt{3}}{24}
=-\frac{50\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{3}}{2*12}=\frac{0+400\sqrt{3}}{24}
=\frac{400\sqrt{3}}{24}
=\frac{50\sqrt{3}}{3}
$