F(x)=-3/2x-3

Solution for F(x)=-3/2x-3 equation:

(F)=-3/2F-3

We move all terms to the left:

(F)-(-3/2F-3)=0


Domain of the equation: 2F-3)!=0

F∈R


We get rid of parentheses

F+3/2F+3=0

We multiply all the terms by the denominator


F*2F+3*2F+3=0

Wy multiply elements

2F^2+6F+3=0

a = 2; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·2·3
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{3}}{2*2}=\frac{-6-2\sqrt{3}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{3}}{2*2}=\frac{-6+2\sqrt{3}}{4}
$