7m^2+32m+17=-7-m^2

Solution for 7m^2+32m+17=-7-m^2 equation:

7m^2+32m+17=-7-m^2

We move all terms to the left:

7m^2+32m+17-(-7-m^2)=0

We get rid of parentheses

7m^2+m^2+32m+7+17=0

We add all the numbers together, and all the variables

8m^2+32m+24=0

a = 8; b = 32; c = +24;
Δ = b2-4ac
Δ = 322-4·8·24
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16}{2*8}=\frac{-48}{16}
=-3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16}{2*8}=\frac{-16}{16}
=-1
$