F(x)=40/3x-34

Solution for F(x)=40/3x-34 equation:

(F)=40/3F-34

We move all terms to the left:

(F)-(40/3F-34)=0


Domain of the equation: 3F-34)!=0

F∈R


We get rid of parentheses

F-40/3F+34=0

We multiply all the terms by the denominator


F*3F+34*3F-40=0

Wy multiply elements

3F^2+102F-40=0

a = 3; b = 102; c = -40;
Δ = b2-4ac
Δ = 1022-4·3·(-40)
Δ = 10884
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:

$\sqrt{\Delta}=\sqrt{10884}=\sqrt{4*2721}=\sqrt{4}*\sqrt{2721}=2\sqrt{2721}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-2\sqrt{2721}}{2*3}=\frac{-102-2\sqrt{2721}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+2\sqrt{2721}}{2*3}=\frac{-102+2\sqrt{2721}}{6}
$