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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8G^2+4G-5=0

a = 8; b = 4; c = -5;
Δ = b2-4ac
Δ = 42-4·8·(-5)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*8}=\frac{-4-4\sqrt{11}}{16}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*8}=\frac{-4+4\sqrt{11}}{16}
$