F(x)=1/4x+9

Solution for F(x)=1/4x+9 equation:

(F)=1/4F+9

We move all terms to the left:

(F)-(1/4F+9)=0


Domain of the equation: 4F+9)!=0

F∈R


We get rid of parentheses

F-1/4F-9=0

We multiply all the terms by the denominator


F*4F-9*4F-1=0

Wy multiply elements

4F^2-36F-1=0

a = 4; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·4·(-1)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{82}}{2*4}=\frac{36-4\sqrt{82}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{82}}{2*4}=\frac{36+4\sqrt{82}}{8}
$