5^2x+7=25^1/3

Solution for 5^2x+7=25^1/3 equation:

5^2x+7=25^1/3

We move all terms to the left:

5^2x+7-(25^1/3)=0

We get rid of parentheses

5^2x+7-25^1/3=0

We multiply all the terms by the denominator


5^2x*3+7*3-25^1=0

We add all the numbers together, and all the variables

5^2x*3-4=0

Wy multiply elements

15x^2-4=0

a = 15; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·15·(-4)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*15}=\frac{0-4\sqrt{15}}{30}
=-\frac{4\sqrt{15}}{30}
=-\frac{2\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*15}=\frac{0+4\sqrt{15}}{30}
=\frac{4\sqrt{15}}{30}
=\frac{2\sqrt{15}}{15}
$