F(x)=-6/7x+8

Solution for F(x)=-6/7x+8 equation:

(F)=-6/7F+8

We move all terms to the left:

(F)-(-6/7F+8)=0


Domain of the equation: 7F+8)!=0

F∈R


We get rid of parentheses

F+6/7F-8=0

We multiply all the terms by the denominator


F*7F-8*7F+6=0

Wy multiply elements

7F^2-56F+6=0

a = 7; b = -56; c = +6;
Δ = b2-4ac
Δ = -562-4·7·6
Δ = 2968
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:

$\sqrt{\Delta}=\sqrt{2968}=\sqrt{4*742}=\sqrt{4}*\sqrt{742}=2\sqrt{742}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{742}}{2*7}=\frac{56-2\sqrt{742}}{14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{742}}{2*7}=\frac{56+2\sqrt{742}}{14}
$