x=4x^2+16x+4

Solution for x=4x^2+16x+4 equation:

x=4x^2+16x+4

We move all terms to the left:

x-(4x^2+16x+4)=0

We get rid of parentheses

-4x^2+x-16x-4=0

We add all the numbers together, and all the variables

-4x^2-15x-4=0

a = -4; b = -15; c = -4;
Δ = b2-4ac
Δ = -152-4·(-4)·(-4)
Δ = 161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{161}}{2*-4}=\frac{15-\sqrt{161}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{161}}{2*-4}=\frac{15+\sqrt{161}}{-8}
$