m^2+30m+20=-7m^2+m-2

Solution for m^2+30m+20=-7m^2+m-2 equation:

m^2+30m+20=-7m^2+m-2

We move all terms to the left:

m^2+30m+20-(-7m^2+m-2)=0

We get rid of parentheses

m^2+7m^2-m+30m+2+20=0

We add all the numbers together, and all the variables

8m^2+29m+22=0

a = 8; b = 29; c = +22;
Δ = b2-4ac
Δ = 292-4·8·22
Δ = 137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{137}}{2*8}=\frac{-29-\sqrt{137}}{16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{137}}{2*8}=\frac{-29+\sqrt{137}}{16}
$