5*3^2x-1+7=42

Solution for 5*3^2x-1+7=42 equation:

5*3^2x-1+7=42

We move all terms to the left:

5*3^2x-1+7-(42)=0

We add all the numbers together, and all the variables

5*3^2x-36=0

Wy multiply elements

15x^2-36=0

a = 15; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·15·(-36)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*15}=\frac{0-12\sqrt{15}}{30}
=-\frac{12\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*15}=\frac{0+12\sqrt{15}}{30}
=\frac{12\sqrt{15}}{30}
=\frac{2\sqrt{15}}{5}
$