14+8g(4g-3)=40

Solution for 14+8g(4g-3)=40 equation:

14+8g(4g-3)=40

We move all terms to the left:

14+8g(4g-3)-(40)=0

We add all the numbers together, and all the variables

8g(4g-3)-26=0

We multiply parentheses

32g^2-24g-26=0

a = 32; b = -24; c = -26;
Δ = b2-4ac
Δ = -242-4·32·(-26)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{61}}{2*32}=\frac{24-8\sqrt{61}}{64}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{61}}{2*32}=\frac{24+8\sqrt{61}}{64}
$