20000=500*2^2x

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Solution for 20000=500*2^2x equation:

20000=500*2^2x
We move all terms to the left:
20000-(500*2^2x)=0
We get rid of parentheses
-500*2^2x+20000=0
Wy multiply elements
-1000x^2+20000=0
a = -1000; b = 0; c = +20000;Δ = b2-4acΔ = 02-4·(-1000)·20000Δ = 80000000The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{80000000}=\sqrt{16000000*5}=\sqrt{16000000}*\sqrt{5}=4000\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4000\sqrt{5}}{2*-1000}=\frac{0-4000\sqrt{5}}{-2000} =-\frac{4000\sqrt{5}}{-2000} =-\frac{2\sqrt{5}}{-1}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4000\sqrt{5}}{2*-1000}=\frac{0+4000\sqrt{5}}{-2000} =\frac{4000\sqrt{5}}{-2000} =\frac{2\sqrt{5}}{-1}$

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