F(x)=-5/2x+4=

Solution for F(x)=-5/2x+4= equation:

(F)=-5/2F+4=

We move all terms to the left:

(F)-(-5/2F+4)=0


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

F∈R


We get rid of parentheses

F+5/2F-4=0

We multiply all the terms by the denominator


F*2F-4*2F+5=0

Wy multiply elements

2F^2-8F+5=0

a = 2; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·2·5
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{6}}{2*2}=\frac{8-2\sqrt{6}}{4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{6}}{2*2}=\frac{8+2\sqrt{6}}{4}
$