G(x)=5x^2-7x-2

Solution for G(x)=5x^2-7x-2 equation:

(G)=5G^2-7G-2

We move all terms to the left:

(G)-(5G^2-7G-2)=0

We get rid of parentheses

-5G^2+G+7G+2=0

We add all the numbers together, and all the variables

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

a = -5; b = 8; c = +2;
Δ = b2-4ac
Δ = 82-4·(-5)·2
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*-5}=\frac{-8-2\sqrt{26}}{-10}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*-5}=\frac{-8+2\sqrt{26}}{-10}
$