F(x)=5/6x+5

Solution for F(x)=5/6x+5 equation:

(F)=5/6F+5

We move all terms to the left:

(F)-(5/6F+5)=0


Domain of the equation: 6F+5)!=0

F∈R


We get rid of parentheses

F-5/6F-5=0

We multiply all the terms by the denominator


F*6F-5*6F-5=0

Wy multiply elements

6F^2-30F-5=0

a = 6; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·6·(-5)
Δ = 1020
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:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{255}}{2*6}=\frac{30-2\sqrt{255}}{12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{255}}{2*6}=\frac{30+2\sqrt{255}}{12}
$