F(x)=-1/4x+3

Solution for F(x)=-1/4x+3 equation:

(F)=-1/4F+3

We move all terms to the left:

(F)-(-1/4F+3)=0


Domain of the equation: 4F+3)!=0

F∈R


We get rid of parentheses

F+1/4F-3=0

We multiply all the terms by the denominator


F*4F-3*4F+1=0

Wy multiply elements

4F^2-12F+1=0

a = 4; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·4·1
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*4}=\frac{12-8\sqrt{2}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*4}=\frac{12+8\sqrt{2}}{8}
$