F(x)=-7/3x+18

Solution for F(x)=-7/3x+18 equation:

(F)=-7/3F+18

We move all terms to the left:

(F)-(-7/3F+18)=0


Domain of the equation: 3F+18)!=0

F∈R


We get rid of parentheses

F+7/3F-18=0

We multiply all the terms by the denominator


F*3F-18*3F+7=0

Wy multiply elements

3F^2-54F+7=0

a = 3; b = -54; c = +7;
Δ = b2-4ac
Δ = -542-4·3·7
Δ = 2832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-4\sqrt{177}}{2*3}=\frac{54-4\sqrt{177}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+4\sqrt{177}}{2*3}=\frac{54+4\sqrt{177}}{6}
$