7a^2=-32a-16

Solution for 7a^2=-32a-16 equation:

7a^2=-32a-16

We move all terms to the left:

7a^2-(-32a-16)=0

We get rid of parentheses

7a^2+32a+16=0

a = 7; b = 32; c = +16;
Δ = b2-4ac
Δ = 322-4·7·16
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-24}{2*7}=\frac{-56}{14}
=-4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+24}{2*7}=\frac{-8}{14}
=-4/7
$