F(x)=210(1.08^x)F(x)=420

Solution for F(x)=210(1.08^x)F(x)=420 equation:

(F)=210(1.08^F)(F)=420

We move all terms to the left:

(F)-(210(1.08^F)(F))=0


We calculate terms in parentheses: -(210(1.08^F)F), so:

210(1.08^F)F

We multiply parentheses

210F^2

Back to the equation:

-(210F^2)


determiningTheFunctionDomain
-210F^2+F=0

a = -210; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-210)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-210}=\frac{-2}{-420}
=1/210
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-210}=\frac{0}{-420}
=0
$