F(x)=3/2x+2

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

(F)=3/2F+2

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

F-3/2F-2=0

We multiply all the terms by the denominator


F*2F-2*2F-3=0

Wy multiply elements

2F^2-4F-3=0

a = 2; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*2}=\frac{4-2\sqrt{10}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*2}=\frac{4+2\sqrt{10}}{4}
$