F(x)=1/5x+6

Solution for F(x)=1/5x+6 equation:

(F)=1/5F+6

We move all terms to the left:

(F)-(1/5F+6)=0


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

F∈R


We get rid of parentheses

F-1/5F-6=0

We multiply all the terms by the denominator


F*5F-6*5F-1=0

Wy multiply elements

5F^2-30F-1=0

a = 5; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·5·(-1)
Δ = 920
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:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{230}}{2*5}=\frac{30-2\sqrt{230}}{10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{230}}{2*5}=\frac{30+2\sqrt{230}}{10}
$