F(x)=-5/3x-8

Solution for F(x)=-5/3x-8 equation:

(F)=-5/3F-8

We move all terms to the left:

(F)-(-5/3F-8)=0


Domain of the equation: 3F-8)!=0

F∈R


We get rid of parentheses

F+5/3F+8=0

We multiply all the terms by the denominator


F*3F+8*3F+5=0

Wy multiply elements

3F^2+24F+5=0

a = 3; b = 24; c = +5;
Δ = b2-4ac
Δ = 242-4·3·5
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{129}}{2*3}=\frac{-24-2\sqrt{129}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{129}}{2*3}=\frac{-24+2\sqrt{129}}{6}
$