G(x)=-2/7x+4

Solution for G(x)=-2/7x+4 equation:

(G)=-2/7G+4

We move all terms to the left:

(G)-(-2/7G+4)=0


Domain of the equation: 7G+4)!=0

G∈R


We get rid of parentheses

G+2/7G-4=0

We multiply all the terms by the denominator


G*7G-4*7G+2=0

Wy multiply elements

7G^2-28G+2=0

a = 7; b = -28; c = +2;
Δ = b2-4ac
Δ = -282-4·7·2
Δ = 728
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:

$\sqrt{\Delta}=\sqrt{728}=\sqrt{4*182}=\sqrt{4}*\sqrt{182}=2\sqrt{182}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{182}}{2*7}=\frac{28-2\sqrt{182}}{14}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{182}}{2*7}=\frac{28+2\sqrt{182}}{14}
$