2x(x-4)+1=6x

Solution for 2x(x-4)+1=6x equation:

2x(x-4)+1=6x

We move all terms to the left:

2x(x-4)+1-(6x)=0

We add all the numbers together, and all the variables

-6x+2x(x-4)+1=0

We multiply parentheses

2x^2-6x-8x+1=0

We add all the numbers together, and all the variables

2x^2-14x+1=0

a = 2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·2·1
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*2}=\frac{14-2\sqrt{47}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*2}=\frac{14+2\sqrt{47}}{4}
$