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 = 636
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:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{159}}{2*3}=\frac{-24-2\sqrt{159}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{159}}{2*3}=\frac{-24+2\sqrt{159}}{6}
$