F(x)=2/3x+8

Solution for F(x)=2/3x+8 equation:

(F)=2/3F+8

We move all terms to the left:

(F)-(2/3F+8)=0


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

F∈R


We get rid of parentheses

F-2/3F-8=0

We multiply all the terms by the denominator


F*3F-8*3F-2=0

Wy multiply elements

3F^2-24F-2=0

a = 3; b = -24; c = -2;
Δ = b2-4ac
Δ = -242-4·3·(-2)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*3}=\frac{24-10\sqrt{6}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*3}=\frac{24+10\sqrt{6}}{6}
$