F(x)=6x-1/5x-2

Solution for F(x)=6x-1/5x-2 equation:

(F)=6F-1/5F-2

We move all terms to the left:

(F)-(6F-1/5F-2)=0


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

F∈R


We get rid of parentheses

F-6F+1/5F+2=0

We multiply all the terms by the denominator


F*5F-6F*5F+2*5F+1=0

Wy multiply elements

5F^2-30F^2+10F+1=0

We add all the numbers together, and all the variables

-25F^2+10F+1=0

a = -25; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-25)·1
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{2}}{2*-25}=\frac{-10-10\sqrt{2}}{-50}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{2}}{2*-25}=\frac{-10+10\sqrt{2}}{-50}
$