G(-7)=x-2/x+11

Solution for G(-7)=x-2/x+11 equation:

(-7)=G-2/G+11

We move all terms to the left:

(-7)-(G-2/G+11)=0


Domain of the equation: G+11)!=0

G∈R


We add all the numbers together, and all the variables

-(G-2/G+11)-7=0

We get rid of parentheses

-G+2/G-11-7=0

We multiply all the terms by the denominator


-G*G-11*G-7*G+2=0

We add all the numbers together, and all the variables

-18G-G*G+2=0

Wy multiply elements

-1G^2-18G+2=0

a = -1; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·(-1)·2
Δ = 332
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{332}=\sqrt{4*83}=\sqrt{4}*\sqrt{83}=2\sqrt{83}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{83}}{2*-1}=\frac{18-2\sqrt{83}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{83}}{2*-1}=\frac{18+2\sqrt{83}}{-2}
$