50=10a(a-5)

Solution for 50=10a(a-5) equation:

50=10a(a-5)

We move all terms to the left:

50-(10a(a-5))=0


We calculate terms in parentheses: -(10a(a-5)), so:

10a(a-5)

We multiply parentheses

10a^2-50a

Back to the equation:

-(10a^2-50a)


We get rid of parentheses

-10a^2+50a+50=0

a = -10; b = 50; c = +50;
Δ = b2-4ac
Δ = 502-4·(-10)·50
Δ = 4500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{5}}{2*-10}=\frac{-50-30\sqrt{5}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{5}}{2*-10}=\frac{-50+30\sqrt{5}}{-20}
$