G(x)=-2/2x+5

Solution for G(x)=-2/2x+5 equation:

(G)=-2/2G+5

We move all terms to the left:

(G)-(-2/2G+5)=0


Domain of the equation: 2G+5)!=0

G∈R


We get rid of parentheses

G+2/2G-5=0

We multiply all the terms by the denominator


G*2G-5*2G+2=0

Wy multiply elements

2G^2-10G+2=0

a = 2; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·2·2
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*2}=\frac{10-2\sqrt{21}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*2}=\frac{10+2\sqrt{21}}{4}
$