G(x)=2x^2+5x-10

Solution for G(x)=2x^2+5x-10 equation:

(G)=2G^2+5G-10

We move all terms to the left:

(G)-(2G^2+5G-10)=0

We get rid of parentheses

-2G^2+G-5G+10=0

We add all the numbers together, and all the variables

-2G^2-4G+10=0

a = -2; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-2)·10
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*-2}=\frac{4-4\sqrt{6}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*-2}=\frac{4+4\sqrt{6}}{-4}
$