F(x)=-3/2x+12

Solution for F(x)=-3/2x+12 equation:

(F)=-3/2F+12

We move all terms to the left:

(F)-(-3/2F+12)=0


Domain of the equation: 2F+12)!=0

F∈R


We get rid of parentheses

F+3/2F-12=0

We multiply all the terms by the denominator


F*2F-12*2F+3=0

Wy multiply elements

2F^2-24F+3=0

a = 2; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·2·3
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{138}}{2*2}=\frac{24-2\sqrt{138}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{138}}{2*2}=\frac{24+2\sqrt{138}}{4}
$