F(x)=-3/2x+4

Solution for F(x)=-3/2x+4 equation:

(F)=-3/2F+4

We move all terms to the left:

(F)-(-3/2F+4)=0


Domain of the equation: 2F+4)!=0

F∈R


We get rid of parentheses

F+3/2F-4=0

We multiply all the terms by the denominator


F*2F-4*2F+3=0

Wy multiply elements

2F^2-8F+3=0

a = 2; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·2·3
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{-(-8)-2\sqrt{10}}{2*2}=\frac{8-2\sqrt{10}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{10}}{2*2}=\frac{8+2\sqrt{10}}{4}
$