(x*(1.085^25))+x=115301

Solution for (x*(1.085^25))+x=115301 equation:

(x(1.085^25))+x=115301

We move all terms to the left:

(x(1.085^25))+x-(115301)=0

We add all the numbers together, and all the variables

x+(x(1.085^25))-115301=0


We calculate terms in parentheses: +(x(1.085^25)), so:

x(1.085^25)

We multiply parentheses

x^2

Back to the equation:

+(x^2)


determiningTheFunctionDomain
x^2+x-115301=0

a = 1; b = 1; c = -115301;
Δ = b2-4ac
Δ = 12-4·1·(-115301)
Δ = 461205
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:

$\sqrt{\Delta}=\sqrt{461205}=\sqrt{9*51245}=\sqrt{9}*\sqrt{51245}=3\sqrt{51245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{51245}}{2*1}=\frac{-1-3\sqrt{51245}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{51245}}{2*1}=\frac{-1+3\sqrt{51245}}{2}
$