4*5^2x=100

Solution for 4*5^2x=100 equation:

4*5^2x=100

We move all terms to the left:

4*5^2x-(100)=0

Wy multiply elements

20x^2-100=0

a = 20; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·20·(-100)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*20}=\frac{0-40\sqrt{5}}{40}
=-\frac{40\sqrt{5}}{40}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*20}=\frac{0+40\sqrt{5}}{40}
=\frac{40\sqrt{5}}{40}
=\sqrt{5}
$