F(0)=x-3/2x-5

Solution for F(0)=x-3/2x-5 equation:

(0)=F-3/2F-5

We move all terms to the left:

(0)-(F-3/2F-5)=0


Domain of the equation: 2F-5)!=0

F∈R


We add all the numbers together, and all the variables

-(F-3/2F-5)=0

We get rid of parentheses

-F+3/2F+5=0

We multiply all the terms by the denominator


-F*2F+5*2F+3=0

Wy multiply elements

-2F^2+10F+3=0

a = -2; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·(-2)·3
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{31}}{2*-2}=\frac{-10-2\sqrt{31}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{31}}{2*-2}=\frac{-10+2\sqrt{31}}{-4}
$