G(x)=1/7x-15

Solution for G(x)=1/7x-15 equation:

(G)=1/7G-15

We move all terms to the left:

(G)-(1/7G-15)=0


Domain of the equation: 7G-15)!=0

G∈R


We get rid of parentheses

G-1/7G+15=0

We multiply all the terms by the denominator


G*7G+15*7G-1=0

Wy multiply elements

7G^2+105G-1=0

a = 7; b = 105; c = -1;
Δ = b2-4ac
Δ = 1052-4·7·(-1)
Δ = 11053
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{-(105)-\sqrt{11053}}{2*7}=\frac{-105-\sqrt{11053}}{14}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11053}}{2*7}=\frac{-105+\sqrt{11053}}{14}
$