5x(x-1)=20

Solution for 5x(x-1)=20 equation:

5x(x-1)=20

We move all terms to the left:

5x(x-1)-(20)=0

We multiply parentheses

5x^2-5x-20=0

a = 5; b = -5; c = -20;
Δ = b2-4ac
Δ = -52-4·5·(-20)
Δ = 425
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{17}}{2*5}=\frac{5-5\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{17}}{2*5}=\frac{5+5\sqrt{17}}{10}
$