G(m)=3m^2+5-8m

Solution for G(m)=3m^2+5-8m equation:

(G)=3G^2+5-8G

We move all terms to the left:

(G)-(3G^2+5-8G)=0

We get rid of parentheses

-3G^2+G+8G-5=0

We add all the numbers together, and all the variables

-3G^2+9G-5=0

a = -3; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-3)·(-5)
Δ = 21
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{-(9)-\sqrt{21}}{2*-3}=\frac{-9-\sqrt{21}}{-6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{21}}{2*-3}=\frac{-9+\sqrt{21}}{-6}
$