25*5^(x)-175=(11250)/(5^(x))

Solution for 25*5^(x)-175=(11250)/(5^(x)) equation:

25*5^(x)-175=(11250)/(5^(x))

We move all terms to the left:

25*5^(x)-175-((11250)/(5^(x)))=0


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

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
25*5^x-(11250/5^x)-175=0

Wy multiply elements

125x-(11250/5^x)-175=0

We get rid of parentheses

125x-11250/5^x-175=0

We multiply all the terms by the denominator


125x*5^x-175*5^x-11250=0

Wy multiply elements

625x^2-875x-11250=0

a = 625; b = -875; c = -11250;
Δ = b2-4ac
Δ = -8752-4·625·(-11250)
Δ = 28890625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28890625}=5375$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-875)-5375}{2*625}=\frac{-4500}{1250}
=-3+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-875)+5375}{2*625}=\frac{6250}{1250}
=5
$