G(x)=10-3/2x

Solution for G(x)=10-3/2x equation:

(G)=10-3/2G

We move all terms to the left:

(G)-(10-3/2G)=0


Domain of the equation: 2G)!=0

G!=0/1

G!=0

G∈R


We add all the numbers together, and all the variables

G-(-3/2G+10)=0

We get rid of parentheses

G+3/2G-10=0

We multiply all the terms by the denominator


G*2G-10*2G+3=0

Wy multiply elements

2G^2-20G+3=0

a = 2; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·2·3
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{94}}{2*2}=\frac{20-2\sqrt{94}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{94}}{2*2}=\frac{20+2\sqrt{94}}{4}
$