5x(2x-1)=2

Solution for 5x(2x-1)=2 equation:

5x(2x-1)=2

We move all terms to the left:

5x(2x-1)-(2)=0

We multiply parentheses

10x^2-5x-2=0

a = 10; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·10·(-2)
Δ = 105
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{105}}{2*10}=\frac{5-\sqrt{105}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*10}=\frac{5+\sqrt{105}}{20}
$