G(x)=-10x^2+3x+27

Solution for G(x)=-10x^2+3x+27 equation:

(G)=-10G^2+3G+27

We move all terms to the left:

(G)-(-10G^2+3G+27)=0

We get rid of parentheses

10G^2-3G+G-27=0

We add all the numbers together, and all the variables

10G^2-2G-27=0

a = 10; b = -2; c = -27;
Δ = b2-4ac
Δ = -22-4·10·(-27)
Δ = 1084
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:

$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{271}}{2*10}=\frac{2-2\sqrt{271}}{20}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{271}}{2*10}=\frac{2+2\sqrt{271}}{20}
$