G(t)=4200-22/3t

Solution for G(t)=4200-22/3t equation:

(G)=4200-22/3G

We move all terms to the left:

(G)-(4200-22/3G)=0


Domain of the equation: 3G)!=0

G!=0/1

G!=0

G∈R


We add all the numbers together, and all the variables

G-(-22/3G+4200)=0

We get rid of parentheses

G+22/3G-4200=0

We multiply all the terms by the denominator


G*3G-4200*3G+22=0

Wy multiply elements

3G^2-12600G+22=0

a = 3; b = -12600; c = +22;
Δ = b2-4ac
Δ = -126002-4·3·22
Δ = 158759736
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:

$\sqrt{\Delta}=\sqrt{158759736}=\sqrt{4*39689934}=\sqrt{4}*\sqrt{39689934}=2\sqrt{39689934}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12600)-2\sqrt{39689934}}{2*3}=\frac{12600-2\sqrt{39689934}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12600)+2\sqrt{39689934}}{2*3}=\frac{12600+2\sqrt{39689934}}{6}
$