F(-3)=6x-1/5x-2

Solution for F(-3)=6x-1/5x-2 equation:

(-3)=6F-1/5F-2

We move all terms to the left:

(-3)-(6F-1/5F-2)=0


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

F∈R


We add all the numbers together, and all the variables

-(6F-1/5F-2)-3=0

We get rid of parentheses

-6F+1/5F+2-3=0

We multiply all the terms by the denominator


-6F*5F+2*5F-3*5F+1=0

Wy multiply elements

-30F^2+10F-15F+1=0

We add all the numbers together, and all the variables

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

a = -30; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-30)·1
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{145}}{2*-30}=\frac{5-\sqrt{145}}{-60}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{145}}{2*-30}=\frac{5+\sqrt{145}}{-60}
$