X+1.6x+(1.6^2)x=200

Solution for X+1.6x+(1.6^2)x=200 equation:

X+1.6X+(1.6^2)X=200

We move all terms to the left:

X+1.6X+(1.6^2)X-(200)=0

We add all the numbers together, and all the variables

2.6X+(1.6^2)X-200=0

We multiply parentheses

X^2+2.6X-200=0

a = 1; b = 2.6; c = -200;
Δ = b2-4ac
Δ = 2.62-4·1·(-200)
Δ = 806.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2.6)-\sqrt{806.76}}{2*1}=\frac{-2.6-\sqrt{806.76}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.6)+\sqrt{806.76}}{2*1}=\frac{-2.6+\sqrt{806.76}}{2}
$