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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·(-2)·(-5)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{6}}{2*-2}=\frac{-8-2\sqrt{6}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{6}}{2*-2}=\frac{-8+2\sqrt{6}}{-4}
$