G(x)=2x^2+7x-10

Solution for G(x)=2x^2+7x-10 equation:

(G)=2G^2+7G-10

We move all terms to the left:

(G)-(2G^2+7G-10)=0

We get rid of parentheses

-2G^2+G-7G+10=0

We add all the numbers together, and all the variables

-2G^2-6G+10=0

a = -2; b = -6; c = +10;
Δ = b2-4ac
Δ = -62-4·(-2)·10
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*-2}=\frac{6-2\sqrt{29}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*-2}=\frac{6+2\sqrt{29}}{-4}
$