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

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

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

We move all terms to the left:

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


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

F∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4F^2-20F^2+8F+2=0

We add all the numbers together, and all the variables

-16F^2+8F+2=0

a = -16; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-16)·2
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{3}}{2*-16}=\frac{-8-8\sqrt{3}}{-32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{3}}{2*-16}=\frac{-8+8\sqrt{3}}{-32}
$