4m^2+9m-45=0

Solution for 4m^2+9m-45=0 equation:

4m^2+9m-45=0

a = 4; b = 9; c = -45;
Δ = b2-4ac
Δ = 92-4·4·(-45)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{89}}{2*4}=\frac{-9-3\sqrt{89}}{8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{89}}{2*4}=\frac{-9+3\sqrt{89}}{8}
$