5x(2x-1)-2(3x)=1

Solution for 5x(2x-1)-2(3x)=1 equation:

5x(2x-1)-2(3x)=1

We move all terms to the left:

5x(2x-1)-2(3x)-(1)=0

We add all the numbers together, and all the variables

-23x+5x(2x-1)-1=0

We multiply parentheses

10x^2-23x-5x-1=0

We add all the numbers together, and all the variables

10x^2-28x-1=0

a = 10; b = -28; c = -1;
Δ = b2-4ac
Δ = -282-4·10·(-1)
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{206}}{2*10}=\frac{28-2\sqrt{206}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{206}}{2*10}=\frac{28+2\sqrt{206}}{20}
$