7=9*5^2x

Solution for 7=9*5^2x equation:

7=9*5^2x

We move all terms to the left:

7-(9*5^2x)=0

We get rid of parentheses

-9*5^2x+7=0

Wy multiply elements

-45x^2+7=0

a = -45; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-45)·7
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{35}}{2*-45}=\frac{0-6\sqrt{35}}{-90}
=-\frac{6\sqrt{35}}{-90}
=-\frac{\sqrt{35}}{-15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*-45}=\frac{0+6\sqrt{35}}{-90}
=\frac{6\sqrt{35}}{-90}
=\frac{\sqrt{35}}{-15}
$