4x^2+4x+1=8x+64

Solution for 4x^2+4x+1=8x+64 equation:

4x^2+4x+1=8x+64

We move all terms to the left:

4x^2+4x+1-(8x+64)=0

We get rid of parentheses

4x^2+4x-8x-64+1=0

We add all the numbers together, and all the variables

4x^2-4x-63=0

a = 4; b = -4; c = -63;
Δ = b2-4ac
Δ = -42-4·4·(-63)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*4}=\frac{36}{8}
=4+1/2
$