(2x)^2=100000

Solution for (2x)^2=100000 equation:

(2x)^2=100000

We move all terms to the left:

(2x)^2-(100000)=0

a = 2; b = 0; c = -100000;
Δ = b2-4ac
Δ = 02-4·2·(-100000)
Δ = 800000
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:

$\sqrt{\Delta}=\sqrt{800000}=\sqrt{160000*5}=\sqrt{160000}*\sqrt{5}=400\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-400\sqrt{5}}{2*2}=\frac{0-400\sqrt{5}}{4}
=-\frac{400\sqrt{5}}{4}
=-100\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+400\sqrt{5}}{2*2}=\frac{0+400\sqrt{5}}{4}
=\frac{400\sqrt{5}}{4}
=100\sqrt{5}
$