F(x)=3/7x-4

Solution for F(x)=3/7x-4 equation:

(F)=3/7F-4

We move all terms to the left:

(F)-(3/7F-4)=0


Domain of the equation: 7F-4)!=0

F∈R


We get rid of parentheses

F-3/7F+4=0

We multiply all the terms by the denominator


F*7F+4*7F-3=0

Wy multiply elements

7F^2+28F-3=0

a = 7; b = 28; c = -3;
Δ = b2-4ac
Δ = 282-4·7·(-3)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{217}}{2*7}=\frac{-28-2\sqrt{217}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{217}}{2*7}=\frac{-28+2\sqrt{217}}{14}
$