F(x)=3x-25/x+5

Solution for F(x)=3x-25/x+5 equation:

(F)=3F-25/F+5

We move all terms to the left:

(F)-(3F-25/F+5)=0


Domain of the equation: F+5)!=0

F∈R


We get rid of parentheses

F-3F+25/F-5=0

We multiply all the terms by the denominator


F*F-3F*F-5*F+25=0

We add all the numbers together, and all the variables

-5F+F*F-3F*F+25=0

Wy multiply elements

F^2-3F^2-5F+25=0

We add all the numbers together, and all the variables

-2F^2-5F+25=0

a = -2; b = -5; c = +25;
Δ = b2-4ac
Δ = -52-4·(-2)·25
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*-2}=\frac{-10}{-4}
=2+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*-2}=\frac{20}{-4}
=-5
$