16x^2=-15-32x

Solution for 16x^2=-15-32x equation:

16x^2=-15-32x

We move all terms to the left:

16x^2-(-15-32x)=0

We add all the numbers together, and all the variables

16x^2-(-32x-15)=0

We get rid of parentheses

16x^2+32x+15=0

a = 16; b = 32; c = +15;
Δ = b2-4ac
Δ = 322-4·16·15
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{-(32)-8}{2*16}=\frac{-40}{32}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8}{2*16}=\frac{-24}{32}
=-3/4
$