4(g+8)g=3

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

4(g+8)g=3

We move all terms to the left:

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

We multiply parentheses

4g^2+32g-3=0

a = 4; b = 32; c = -3;
Δ = b2-4ac
Δ = 322-4·4·(-3)
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{67}}{2*4}=\frac{-32-4\sqrt{67}}{8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{67}}{2*4}=\frac{-32+4\sqrt{67}}{8}
$