5^x-3=16/5^x+3

Solution for 5^x-3=16/5^x+3 equation:

5^x-3=16/5^x+3

We move all terms to the left:

5^x-3-(16/5^x+3)=0


Domain of the equation: 5^x+3)!=0

x∈R


We get rid of parentheses

5^x-16/5^x-3-3=0

We multiply all the terms by the denominator


5^x*5^x-3*5^x-3*5^x-16=0

Wy multiply elements

25x^2-15x-15x-16=0

We add all the numbers together, and all the variables

25x^2-30x-16=0

a = 25; b = -30; c = -16;
Δ = b2-4ac
Δ = -302-4·25·(-16)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-50}{2*25}=\frac{-20}{50}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+50}{2*25}=\frac{80}{50}
=1+3/5
$