5^2x=65/3

Solution for 5^2x=65/3 equation:

5^2x=65/3

We move all terms to the left:

5^2x-(65/3)=0

We add all the numbers together, and all the variables

5^2x-(+65/3)=0

We get rid of parentheses

5^2x-65/3=0

We multiply all the terms by the denominator


5^2x*3-65=0

Wy multiply elements

15x^2-65=0

a = 15; b = 0; c = -65;
Δ = b2-4ac
Δ = 02-4·15·(-65)
Δ = 3900
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:

$\sqrt{\Delta}=\sqrt{3900}=\sqrt{100*39}=\sqrt{100}*\sqrt{39}=10\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{39}}{2*15}=\frac{0-10\sqrt{39}}{30}
=-\frac{10\sqrt{39}}{30}
=-\frac{\sqrt{39}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{39}}{2*15}=\frac{0+10\sqrt{39}}{30}
=\frac{10\sqrt{39}}{30}
=\frac{\sqrt{39}}{3}
$