25,000=10,000(1.08^)9x

Solution for 25,000=10,000(1.08^)9x equation:

25.000=10.000(1.08^)9x

We move all terms to the left:

25.000-(10.000(1.08^)9x)=0

We add all the numbers together, and all the variables

-(10.000(1.08^)9x)+25=0


We calculate terms in parentheses: -(10.000(1.08^)9x), so:

10.000(1.08^)9x

We multiply parentheses

90x^2

Back to the equation:

-(90x^2)


a = -90; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-90)·25
Δ = 9000
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:

$\sqrt{\Delta}=\sqrt{9000}=\sqrt{900*10}=\sqrt{900}*\sqrt{10}=30\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{10}}{2*-90}=\frac{0-30\sqrt{10}}{-180}
=-\frac{30\sqrt{10}}{-180}
=-\frac{\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{10}}{2*-90}=\frac{0+30\sqrt{10}}{-180}
=\frac{30\sqrt{10}}{-180}
=\frac{\sqrt{10}}{-6}
$