5(3^2x+2)=31

Solution for 5(3^2x+2)=31 equation:

5(3^2x+2)=31

We move all terms to the left:

5(3^2x+2)-(31)=0

We multiply parentheses

15x^2+10-31=0

We add all the numbers together, and all the variables

15x^2-21=0

a = 15; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·15·(-21)
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*15}=\frac{0-6\sqrt{35}}{30}
=-\frac{6\sqrt{35}}{30}
=-\frac{\sqrt{35}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{35}}{2*15}=\frac{0+6\sqrt{35}}{30}
=\frac{6\sqrt{35}}{30}
=\frac{\sqrt{35}}{5}
$