5m2=14-9m

Solution for 5m2=14-9m equation:

5m^2=14-9m

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5m^2+9m-14=0

a = 5; b = 9; c = -14;
Δ = b2-4ac
Δ = 92-4·5·(-14)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-19}{2*5}=\frac{-28}{10}
=-2+4/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+19}{2*5}=\frac{10}{10}
=1
$