F(x)=-9/4x-8

Solution for F(x)=-9/4x-8 equation:

(F)=-9/4F-8

We move all terms to the left:

(F)-(-9/4F-8)=0


Domain of the equation: 4F-8)!=0

F∈R


We get rid of parentheses

F+9/4F+8=0

We multiply all the terms by the denominator


F*4F+8*4F+9=0

Wy multiply elements

4F^2+32F+9=0

a = 4; b = 32; c = +9;
Δ = b2-4ac
Δ = 322-4·4·9
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{55}}{2*4}=\frac{-32-4\sqrt{55}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{55}}{2*4}=\frac{-32+4\sqrt{55}}{8}
$