(1)/(3)10^(2x)=12

Solution for (1)/(3)10^(2x)=12 equation:

(1)/(3)10^(2x)=12

We move all terms to the left:

(1)/(3)10^(2x)-(12)=0


Domain of the equation: 310^2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-12*310^2x+1=0

Wy multiply elements

-3720x^2+1=0

a = -3720; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-3720)·1
Δ = 14880
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:

$\sqrt{\Delta}=\sqrt{14880}=\sqrt{16*930}=\sqrt{16}*\sqrt{930}=4\sqrt{930}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{930}}{2*-3720}=\frac{0-4\sqrt{930}}{-7440}
=-\frac{4\sqrt{930}}{-7440}
=-\frac{\sqrt{930}}{-1860}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{930}}{2*-3720}=\frac{0+4\sqrt{930}}{-7440}
=\frac{4\sqrt{930}}{-7440}
=\frac{\sqrt{930}}{-1860}
$