G(x+4)=3/4x+5

Solution for G(x+4)=3/4x+5 equation:

(G+4)=3/4G+5

We move all terms to the left:

(G+4)-(3/4G+5)=0


Domain of the equation: 4G+5)!=0

G∈R


We get rid of parentheses

G-3/4G+4-5=0

We multiply all the terms by the denominator


G*4G+4*4G-5*4G-3=0

Wy multiply elements

4G^2+16G-20G-3=0

We add all the numbers together, and all the variables

4G^2-4G-3=0

a = 4; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·4·(-3)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*4}=\frac{-4}{8}
=-1/2
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*4}=\frac{12}{8}
=1+1/2
$