F(x)=4/3x-16

Solution for F(x)=4/3x-16 equation:

(F)=4/3F-16

We move all terms to the left:

(F)-(4/3F-16)=0


Domain of the equation: 3F-16)!=0

F∈R


We get rid of parentheses

F-4/3F+16=0

We multiply all the terms by the denominator


F*3F+16*3F-4=0

Wy multiply elements

3F^2+48F-4=0

a = 3; b = 48; c = -4;
Δ = b2-4ac
Δ = 482-4·3·(-4)
Δ = 2352
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:

$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-28\sqrt{3}}{2*3}=\frac{-48-28\sqrt{3}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+28\sqrt{3}}{2*3}=\frac{-48+28\sqrt{3}}{6}
$