50=10b(b+2)

Solution for 50=10b(b+2) equation:

50=10b(b+2)

We move all terms to the left:

50-(10b(b+2))=0


We calculate terms in parentheses: -(10b(b+2)), so:

10b(b+2)

We multiply parentheses

10b^2+20b

Back to the equation:

-(10b^2+20b)


We get rid of parentheses

-10b^2-20b+50=0

a = -10; b = -20; c = +50;
Δ = b2-4ac
Δ = -202-4·(-10)·50
Δ = 2400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{6}}{2*-10}=\frac{20-20\sqrt{6}}{-20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{6}}{2*-10}=\frac{20+20\sqrt{6}}{-20}
$