20=4g(g-15)

Solution for 20=4g(g-15) equation:

20=4g(g-15)

We move all terms to the left:

20-(4g(g-15))=0


We calculate terms in parentheses: -(4g(g-15)), so:

4g(g-15)

We multiply parentheses

4g^2-60g

Back to the equation:

-(4g^2-60g)


We get rid of parentheses

-4g^2+60g+20=0

a = -4; b = 60; c = +20;
Δ = b2-4ac
Δ = 602-4·(-4)·20
Δ = 3920
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:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-28\sqrt{5}}{2*-4}=\frac{-60-28\sqrt{5}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+28\sqrt{5}}{2*-4}=\frac{-60+28\sqrt{5}}{-8}
$