-5g(-8-g)=12

Solution for -5g(-8-g)=12 equation:

-5g(-8-g)=12

We move all terms to the left:

-5g(-8-g)-(12)=0

We add all the numbers together, and all the variables

-5g(-1g-8)-12=0

We multiply parentheses

5g^2+40g-12=0

a = 5; b = 40; c = -12;
Δ = b2-4ac
Δ = 402-4·5·(-12)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{115}}{2*5}=\frac{-40-4\sqrt{115}}{10}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{115}}{2*5}=\frac{-40+4\sqrt{115}}{10}
$