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

Solution for -5g(-1)(8-g)=12 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

-5g(g-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 = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{85}}{2*-5}=\frac{-40-4\sqrt{85}}{-10}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{85}}{2*-5}=\frac{-40+4\sqrt{85}}{-10}
$