F(x)=4/7x+1

Solution for F(x)=4/7x+1 equation:

(F)=4/7F+1

We move all terms to the left:

(F)-(4/7F+1)=0


Domain of the equation: 7F+1)!=0

F∈R


We get rid of parentheses

F-4/7F-1=0

We multiply all the terms by the denominator


F*7F-1*7F-4=0

Wy multiply elements

7F^2-7F-4=0

a = 7; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·7·(-4)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{161}}{2*7}=\frac{7-\sqrt{161}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{161}}{2*7}=\frac{7+\sqrt{161}}{14}
$