4x^2=8x+1

Solution for 4x^2=8x+1 equation:

4x^2=8x+1

We move all terms to the left:

4x^2-(8x+1)=0

We get rid of parentheses

4x^2-8x-1=0

a = 4; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·4·(-1)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*4}=\frac{8-4\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*4}=\frac{8+4\sqrt{5}}{8}
$