10*10^(2x)=12

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

10*10^(2x)=12

We move all terms to the left:

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

Wy multiply elements

100x^2-12=0

a = 100; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·100·(-12)
Δ = 4800
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:

$\sqrt{\Delta}=\sqrt{4800}=\sqrt{1600*3}=\sqrt{1600}*\sqrt{3}=40\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{3}}{2*100}=\frac{0-40\sqrt{3}}{200}
=-\frac{40\sqrt{3}}{200}
=-\frac{\sqrt{3}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{3}}{2*100}=\frac{0+40\sqrt{3}}{200}
=\frac{40\sqrt{3}}{200}
=\frac{\sqrt{3}}{5}
$