-3*10^(2t)=-28

Solution for -3*10^(2t)=-28 equation:

-3*10^(2t)=-28

We move all terms to the left:

-3*10^(2t)-(-28)=0

We add all the numbers together, and all the variables

-3*10^2t+28=0

Wy multiply elements

-30t^2+28=0

a = -30; b = 0; c = +28;
Δ = b2-4ac
Δ = 02-4·(-30)·28
Δ = 3360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{210}}{2*-30}=\frac{0-4\sqrt{210}}{-60}
=-\frac{4\sqrt{210}}{-60}
=-\frac{\sqrt{210}}{-15}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{210}}{2*-30}=\frac{0+4\sqrt{210}}{-60}
=\frac{4\sqrt{210}}{-60}
=\frac{\sqrt{210}}{-15}
$