9m^2+47m-7=-5m^2

Solution for 9m^2+47m-7=-5m^2 equation:

9m^2+47m-7=-5m^2

We move all terms to the left:

9m^2+47m-7-(-5m^2)=0

We get rid of parentheses

9m^2+5m^2+47m-7=0

We add all the numbers together, and all the variables

14m^2+47m-7=0

a = 14; b = 47; c = -7;
Δ = b2-4ac
Δ = 472-4·14·(-7)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-51}{2*14}=\frac{-98}{28}
=-3+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+51}{2*14}=\frac{4}{28}
=1/7
$