2x(x-34)=1

Solution for 2x(x-34)=1 equation:

2x(x-34)=1

We move all terms to the left:

2x(x-34)-(1)=0

We multiply parentheses

2x^2-68x-1=0

a = 2; b = -68; c = -1;
Δ = b2-4ac
Δ = -682-4·2·(-1)
Δ = 4632
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:

$\sqrt{\Delta}=\sqrt{4632}=\sqrt{4*1158}=\sqrt{4}*\sqrt{1158}=2\sqrt{1158}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-2\sqrt{1158}}{2*2}=\frac{68-2\sqrt{1158}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+2\sqrt{1158}}{2*2}=\frac{68+2\sqrt{1158}}{4}
$