F(x)=3/2x-6

Solution for F(x)=3/2x-6 equation:

(F)=3/2F-6

We move all terms to the left:

(F)-(3/2F-6)=0


Domain of the equation: 2F-6)!=0

F∈R


We get rid of parentheses

F-3/2F+6=0

We multiply all the terms by the denominator


F*2F+6*2F-3=0

Wy multiply elements

2F^2+12F-3=0

a = 2; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·2·(-3)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*2}=\frac{-12-2\sqrt{42}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*2}=\frac{-12+2\sqrt{42}}{4}
$