9m^2=5m+16

Solution for 9m^2=5m+16 equation:

9m^2=5m+16

We move all terms to the left:

9m^2-(5m+16)=0

We get rid of parentheses

9m^2-5m-16=0

a = 9; b = -5; c = -16;
Δ = b2-4ac
Δ = -52-4·9·(-16)
Δ = 601
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{-(-5)-\sqrt{601}}{2*9}=\frac{5-\sqrt{601}}{18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{601}}{2*9}=\frac{5+\sqrt{601}}{18}
$