2(m2+14m+48)+9(m2+14m+48)-5=0

Solution for 2(m2+14m+48)+9(m2+14m+48)-5=0 equation:

2(m2+14m+48)+9(m2+14m+48)-5=0

We add all the numbers together, and all the variables

2(+m^2+14m+48)+9(+m^2+14m+48)-5=0

We multiply parentheses

2m^2+9m^2+28m+126m+96+432-5=0

We add all the numbers together, and all the variables

11m^2+154m+523=0

a = 11; b = 154; c = +523;
Δ = b2-4ac
Δ = 1542-4·11·523
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(154)-8\sqrt{11}}{2*11}=\frac{-154-8\sqrt{11}}{22}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(154)+8\sqrt{11}}{2*11}=\frac{-154+8\sqrt{11}}{22}
$