F(x)=14/2x+24

Solution for F(x)=14/2x+24 equation:

(F)=14/2F+24

We move all terms to the left:

(F)-(14/2F+24)=0


Domain of the equation: 2F+24)!=0

F∈R


We get rid of parentheses

F-14/2F-24=0

We multiply all the terms by the denominator


F*2F-24*2F-14=0

Wy multiply elements

2F^2-48F-14=0

a = 2; b = -48; c = -14;
Δ = b2-4ac
Δ = -482-4·2·(-14)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{151}}{2*2}=\frac{48-4\sqrt{151}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{151}}{2*2}=\frac{48+4\sqrt{151}}{4}
$