x+1.1x+(1.1^2)x=90

Solution for x+1.1x+(1.1^2)x=90 equation:

x+1.1x+(1.1^2)x=90

We move all terms to the left:

x+1.1x+(1.1^2)x-(90)=0

We add all the numbers together, and all the variables

2.1x+(1.1^2)x-90=0

We multiply parentheses

x^2+2.1x-90=0

a = 1; b = 2.1; c = -90;
Δ = b2-4ac
Δ = 2.12-4·1·(-90)
Δ = 364.41
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{-(2.1)-\sqrt{364.41}}{2*1}=\frac{-2.1-\sqrt{364.41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.1)+\sqrt{364.41}}{2*1}=\frac{-2.1+\sqrt{364.41}}{2}
$