15m^2-10m-9=0

Solution for 15m^2-10m-9=0 equation:

15m^2-10m-9=0

a = 15; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·15·(-9)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-8\sqrt{10}}{2*15}=\frac{10-8\sqrt{10}}{30}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+8\sqrt{10}}{2*15}=\frac{10+8\sqrt{10}}{30}
$