3=16x^2+4x

Solution for 3=16x^2+4x equation:

3=16x^2+4x

We move all terms to the left:

3-(16x^2+4x)=0

We get rid of parentheses

-16x^2-4x+3=0

a = -16; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·(-16)·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{13}}{2*-16}=\frac{4-4\sqrt{13}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{13}}{2*-16}=\frac{4+4\sqrt{13}}{-32}
$