G(x)=x^2-11x+24

Solution for G(x)=x^2-11x+24 equation:

(G)=G^2-11G+24

We move all terms to the left:

(G)-(G^2-11G+24)=0

We get rid of parentheses

-G^2+G+11G-24=0

We add all the numbers together, and all the variables

-1G^2+12G-24=0

a = -1; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·(-1)·(-24)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{3}}{2*-1}=\frac{-12-4\sqrt{3}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{3}}{2*-1}=\frac{-12+4\sqrt{3}}{-2}
$