G(x)=32/5x+55

Solution for G(x)=32/5x+55 equation:

(G)=32/5G+55

We move all terms to the left:

(G)-(32/5G+55)=0


Domain of the equation: 5G+55)!=0

G∈R


We get rid of parentheses

G-32/5G-55=0

We multiply all the terms by the denominator


G*5G-55*5G-32=0

Wy multiply elements

5G^2-275G-32=0

a = 5; b = -275; c = -32;
Δ = b2-4ac
Δ = -2752-4·5·(-32)
Δ = 76265
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{-(-275)-\sqrt{76265}}{2*5}=\frac{275-\sqrt{76265}}{10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-275)+\sqrt{76265}}{2*5}=\frac{275+\sqrt{76265}}{10}
$