F(x)=-4/3x+8

Solution for F(x)=-4/3x+8 equation:

(F)=-4/3F+8

We move all terms to the left:

(F)-(-4/3F+8)=0


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

F∈R


We get rid of parentheses

F+4/3F-8=0

We multiply all the terms by the denominator


F*3F-8*3F+4=0

Wy multiply elements

3F^2-24F+4=0

a = 3; b = -24; c = +4;
Δ = b2-4ac
Δ = -242-4·3·4
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{33}}{2*3}=\frac{24-4\sqrt{33}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{33}}{2*3}=\frac{24+4\sqrt{33}}{6}
$