5*5^2x=30

Solution for 5*5^2x=30 equation:

5*5^2x=30

We move all terms to the left:

5*5^2x-(30)=0

Wy multiply elements

25x^2-30=0

a = 25; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·25·(-30)
Δ = 3000
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:

$\sqrt{\Delta}=\sqrt{3000}=\sqrt{100*30}=\sqrt{100}*\sqrt{30}=10\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{30}}{2*25}=\frac{0-10\sqrt{30}}{50}
=-\frac{10\sqrt{30}}{50}
=-\frac{\sqrt{30}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{30}}{2*25}=\frac{0+10\sqrt{30}}{50}
=\frac{10\sqrt{30}}{50}
=\frac{\sqrt{30}}{5}
$