F(x)=1-7x/6x+5

Solution for F(x)=1-7x/6x+5 equation:

(F)=1-7F/6F+5

We move all terms to the left:

(F)-(1-7F/6F+5)=0


Domain of the equation: 6F+5)!=0

F∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

F+7F/6F-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

6F^2+7F-36F=0

We add all the numbers together, and all the variables

6F^2-29F=0

a = 6; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·6·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*6}=\frac{0}{12}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*6}=\frac{58}{12}
=4+5/6
$