16x+3=-16x^2

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

16x+3=-16x^2

We move all terms to the left:

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

We get rid of parentheses

16x^2+16x+3=0

a = 16; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·16·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*16}=\frac{-24}{32}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*16}=\frac{-8}{32}
=-1/4
$