4x^2-80x=1

Solution for 4x^2-80x=1 equation:

4x^2-80x=1

We move all terms to the left:

4x^2-80x-(1)=0

a = 4; b = -80; c = -1;
Δ = b2-4ac
Δ = -802-4·4·(-1)
Δ = 6416
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:

$\sqrt{\Delta}=\sqrt{6416}=\sqrt{16*401}=\sqrt{16}*\sqrt{401}=4\sqrt{401}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{401}}{2*4}=\frac{80-4\sqrt{401}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{401}}{2*4}=\frac{80+4\sqrt{401}}{8}
$