F(x)=3/4x+9

Solution for F(x)=3/4x+9 equation:

(F)=3/4F+9

We move all terms to the left:

(F)-(3/4F+9)=0


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

F∈R


We get rid of parentheses

F-3/4F-9=0

We multiply all the terms by the denominator


F*4F-9*4F-3=0

Wy multiply elements

4F^2-36F-3=0

a = 4; b = -36; c = -3;
Δ = b2-4ac
Δ = -362-4·4·(-3)
Δ = 1344
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:

$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-8\sqrt{21}}{2*4}=\frac{36-8\sqrt{21}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+8\sqrt{21}}{2*4}=\frac{36+8\sqrt{21}}{8}
$