F(2)=4x-10/x+2

Solution for F(2)=4x-10/x+2 equation:

(2)=4F-10/F+2

We move all terms to the left:

(2)-(4F-10/F+2)=0


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

F∈R


We get rid of parentheses

-4F+10/F-2+2=0

We multiply all the terms by the denominator


-4F*F-2*F+2*F+10=0

We add all the numbers together, and all the variables

-4F*F+10=0

Wy multiply elements

-4F^2+10=0

a = -4; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-4)·10
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-4}=\frac{0-4\sqrt{10}}{-8}
=-\frac{4\sqrt{10}}{-8}
=-\frac{\sqrt{10}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-4}=\frac{0+4\sqrt{10}}{-8}
=\frac{4\sqrt{10}}{-8}
=\frac{\sqrt{10}}{-2}
$