F(x)=9/7x-3

Solution for F(x)=9/7x-3 equation:

(F)=9/7F-3

We move all terms to the left:

(F)-(9/7F-3)=0


Domain of the equation: 7F-3)!=0

F∈R


We get rid of parentheses

F-9/7F+3=0

We multiply all the terms by the denominator


F*7F+3*7F-9=0

Wy multiply elements

7F^2+21F-9=0

a = 7; b = 21; c = -9;
Δ = b2-4ac
Δ = 212-4·7·(-9)
Δ = 693
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:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{77}}{2*7}=\frac{-21-3\sqrt{77}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{77}}{2*7}=\frac{-21+3\sqrt{77}}{14}
$