F(x)=5+7x/4x-12

Solution for F(x)=5+7x/4x-12 equation:

(F)=5+7F/4F-12

We move all terms to the left:

(F)-(5+7F/4F-12)=0


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

F∈R


We add all the numbers together, and all the variables

F-(7F/4F-7)=0

We get rid of parentheses

F-7F/4F+7=0

We multiply all the terms by the denominator


F*4F-7F+7*4F=0

We add all the numbers together, and all the variables

-7F+F*4F+7*4F=0

Wy multiply elements

4F^2-7F+28F=0

We add all the numbers together, and all the variables

4F^2+21F=0

a = 4; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·4·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*4}=\frac{-42}{8}
=-5+1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*4}=\frac{0}{8}
=0
$