G(x)=6x+3/10x+5

Solution for G(x)=6x+3/10x+5 equation:

(G)=6G+3/10G+5

We move all terms to the left:

(G)-(6G+3/10G+5)=0


Domain of the equation: 10G+5)!=0

G∈R


We get rid of parentheses

G-6G-3/10G-5=0

We multiply all the terms by the denominator


G*10G-6G*10G-5*10G-3=0

Wy multiply elements

10G^2-60G^2-50G-3=0

We add all the numbers together, and all the variables

-50G^2-50G-3=0

a = -50; b = -50; c = -3;
Δ = b2-4ac
Δ = -502-4·(-50)·(-3)
Δ = 1900
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:

$\sqrt{\Delta}=\sqrt{1900}=\sqrt{100*19}=\sqrt{100}*\sqrt{19}=10\sqrt{19}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{19}}{2*-50}=\frac{50-10\sqrt{19}}{-100}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{19}}{2*-50}=\frac{50+10\sqrt{19}}{-100}
$