5x(10X-5)=1

Solution for 5x(10X-5)=1 equation:

5x(10x-5)=1

We move all terms to the left:

5x(10x-5)-(1)=0

We multiply parentheses

50x^2-25x-1=0

a = 50; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·50·(-1)
Δ = 825
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:

$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{33}}{2*50}=\frac{25-5\sqrt{33}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{33}}{2*50}=\frac{25+5\sqrt{33}}{100}
$