F(x)=7x-3/6x+12

Solution for F(x)=7x-3/6x+12 equation:

(F)=7F-3/6F+12

We move all terms to the left:

(F)-(7F-3/6F+12)=0


Domain of the equation: 6F+12)!=0

F∈R


We get rid of parentheses

F-7F+3/6F-12=0

We multiply all the terms by the denominator


F*6F-7F*6F-12*6F+3=0

Wy multiply elements

6F^2-42F^2-72F+3=0

We add all the numbers together, and all the variables

-36F^2-72F+3=0

a = -36; b = -72; c = +3;
Δ = b2-4ac
Δ = -722-4·(-36)·3
Δ = 5616
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:

$\sqrt{\Delta}=\sqrt{5616}=\sqrt{144*39}=\sqrt{144}*\sqrt{39}=12\sqrt{39}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{39}}{2*-36}=\frac{72-12\sqrt{39}}{-72}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{39}}{2*-36}=\frac{72+12\sqrt{39}}{-72}
$