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 = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*3}=\frac{24-4\sqrt{39}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*3}=\frac{24+4\sqrt{39}}{6}
$