4=12x+16x^2

Solution for 4=12x+16x^2 equation:

4=12x+16x^2

We move all terms to the left:

4-(12x+16x^2)=0

We get rid of parentheses

-16x^2-12x+4=0

a = -16; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-16)·4
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*-16}=\frac{-8}{-32}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*-16}=\frac{32}{-32}
=-1
$