F(-2)=x-10/4x+12

Solution for F(-2)=x-10/4x+12 equation:

(-2)=F-10/4F+12

We move all terms to the left:

(-2)-(F-10/4F+12)=0


Domain of the equation: 4F+12)!=0

F∈R


We add all the numbers together, and all the variables

-(F-10/4F+12)-2=0

We get rid of parentheses

-F+10/4F-12-2=0

We multiply all the terms by the denominator


-F*4F-12*4F-2*4F+10=0

Wy multiply elements

-4F^2-48F-8F+10=0

We add all the numbers together, and all the variables

-4F^2-56F+10=0

a = -4; b = -56; c = +10;
Δ = b2-4ac
Δ = -562-4·(-4)·10
Δ = 3296
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:

$\sqrt{\Delta}=\sqrt{3296}=\sqrt{16*206}=\sqrt{16}*\sqrt{206}=4\sqrt{206}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{206}}{2*-4}=\frac{56-4\sqrt{206}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{206}}{2*-4}=\frac{56+4\sqrt{206}}{-8}
$