G(x)=2x^2+13x+15

Solution for G(x)=2x^2+13x+15 equation:

(G)=2G^2+13G+15

We move all terms to the left:

(G)-(2G^2+13G+15)=0

We get rid of parentheses

-2G^2+G-13G-15=0

We add all the numbers together, and all the variables

-2G^2-12G-15=0

a = -2; b = -12; c = -15;
Δ = b2-4ac
Δ = -122-4·(-2)·(-15)
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{-(-12)-2\sqrt{6}}{2*-2}=\frac{12-2\sqrt{6}}{-4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{6}}{2*-2}=\frac{12+2\sqrt{6}}{-4}
$