G^-1(x)=7x-8/3x+1

Solution for G^-1(x)=7x-8/3x+1 equation:

^-1(G)=7G-8/3G+1

We move all terms to the left:

^-1(G)-(7G-8/3G+1)=0


Domain of the equation: 3G+1)!=0

G∈R


We add all the numbers together, and all the variables

-1G-(7G-8/3G+1)=0

We get rid of parentheses

-1G-7G+8/3G-1=0

We multiply all the terms by the denominator


-1G*3G-7G*3G-1*3G+8=0

Wy multiply elements

-3G^2-21G^2-3G+8=0

We add all the numbers together, and all the variables

-24G^2-3G+8=0

a = -24; b = -3; c = +8;
Δ = b2-4ac
Δ = -32-4·(-24)·8
Δ = 777
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{-(-3)-\sqrt{777}}{2*-24}=\frac{3-\sqrt{777}}{-48}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{777}}{2*-24}=\frac{3+\sqrt{777}}{-48}
$