G(-1)=x-7/x+12

Solution for G(-1)=x-7/x+12 equation:

(-1)=G-7/G+12

We move all terms to the left:

(-1)-(G-7/G+12)=0


Domain of the equation: G+12)!=0

G∈R


We add all the numbers together, and all the variables

-(G-7/G+12)-1=0

We get rid of parentheses

-G+7/G-12-1=0

We multiply all the terms by the denominator


-G*G-12*G-1*G+7=0

We add all the numbers together, and all the variables

-13G-G*G+7=0

Wy multiply elements

-1G^2-13G+7=0

a = -1; b = -13; c = +7;
Δ = b2-4ac
Δ = -132-4·(-1)·7
Δ = 197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{197}}{2*-1}=\frac{13-\sqrt{197}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{197}}{2*-1}=\frac{13+\sqrt{197}}{-2}
$