100=5x(x-1)

Solution for 100=5x(x-1) equation:

100=5x(x-1)

We move all terms to the left:

100-(5x(x-1))=0


We calculate terms in parentheses: -(5x(x-1)), so:

5x(x-1)

We multiply parentheses

5x^2-5x

Back to the equation:

-(5x^2-5x)


We get rid of parentheses

-5x^2+5x+100=0

a = -5; b = 5; c = +100;
Δ = b2-4ac
Δ = 52-4·(-5)·100
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-45}{2*-5}=\frac{-50}{-10}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+45}{2*-5}=\frac{40}{-10}
=-4
$