x(1.08^17)=150000

Solution for x(1.08^17)=150000 equation:

x(1.08^17)=150000

We move all terms to the left:

x(1.08^17)-(150000)=0

We multiply parentheses

x^2-150000=0

a = 1; b = 0; c = -150000;
Δ = b2-4ac
Δ = 02-4·1·(-150000)
Δ = 600000
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:

$\sqrt{\Delta}=\sqrt{600000}=\sqrt{40000*15}=\sqrt{40000}*\sqrt{15}=200\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200\sqrt{15}}{2*1}=\frac{0-200\sqrt{15}}{2}
=-\frac{200\sqrt{15}}{2}
=-100\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200\sqrt{15}}{2*1}=\frac{0+200\sqrt{15}}{2}
=\frac{200\sqrt{15}}{2}
=100\sqrt{15}
$