5g(4/5g+31)=30

Solution for 5g(4/5g+31)=30 equation:

5g(4/5g+31)=30

We move all terms to the left:

5g(4/5g+31)-(30)=0


Domain of the equation: 5g+31)!=0

g∈R


We multiply parentheses

20g^2+155g-30=0

a = 20; b = 155; c = -30;
Δ = b2-4ac
Δ = 1552-4·20·(-30)
Δ = 26425
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:

$\sqrt{\Delta}=\sqrt{26425}=\sqrt{25*1057}=\sqrt{25}*\sqrt{1057}=5\sqrt{1057}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(155)-5\sqrt{1057}}{2*20}=\frac{-155-5\sqrt{1057}}{40}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(155)+5\sqrt{1057}}{2*20}=\frac{-155+5\sqrt{1057}}{40}
$