5g(g+2)=25

Solution for 5g(g+2)=25 equation:

5g(g+2)=25

We move all terms to the left:

5g(g+2)-(25)=0

We multiply parentheses

5g^2+10g-25=0

a = 5; b = 10; c = -25;
Δ = b2-4ac
Δ = 102-4·5·(-25)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{6}}{2*5}=\frac{-10-10\sqrt{6}}{10}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{6}}{2*5}=\frac{-10+10\sqrt{6}}{10}
$