x+(.831648x)/(1.02^(2))=162904.34

Solution for x+(.831648x)/(1.02^(2))=162904.34 equation:

x+(.831648x)/(1.02^(2))=162904.34

We move all terms to the left:

x+(.831648x)/(1.02^(2))-(162904.34)=0

We add all the numbers together, and all the variables

x+(+.831648x)/(1.02^2)-(162904.34)=0

We add all the numbers together, and all the variables

x+(+.831648x)/(1.02^2)-162904.34=0

We multiply all the terms by the denominator


x*(1.02^2)+(+.831648x)-(162904.34)*(1.02^2)=0

We add all the numbers together, and all the variables

x*(1.02^2)+(+.831648x)-169485.675336=0

We multiply parentheses

x^2+(+.831648x)-169485.675336=0

We get rid of parentheses

x^2+.831648x-169485.675336=0

a = 1; b = .831648; c = -169485.675336;
Δ = b2-4ac
Δ = .8316482-4·1·(-169485.675336)
Δ = 677943.3929824
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{-(.831648)-\sqrt{677943.3929824}}{2*1}=\frac{-0.831648-\sqrt{677943.3929824}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(.831648)+\sqrt{677943.3929824}}{2*1}=\frac{-0.831648+\sqrt{677943.3929824}}{2}
$