F(x)=-3/4x-6

Solution for F(x)=-3/4x-6 equation:

(F)=-3/4F-6

We move all terms to the left:

(F)-(-3/4F-6)=0


Domain of the equation: 4F-6)!=0

F∈R


We get rid of parentheses

F+3/4F+6=0

We multiply all the terms by the denominator


F*4F+6*4F+3=0

Wy multiply elements

4F^2+24F+3=0

a = 4; b = 24; c = +3;
Δ = b2-4ac
Δ = 242-4·4·3
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{33}}{2*4}=\frac{-24-4\sqrt{33}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{33}}{2*4}=\frac{-24+4\sqrt{33}}{8}
$