(5m-2)(3m+4)=0

Solution for (5m-2)(3m+4)=0 equation:

(5m-2)(3m+4)=0

We multiply parentheses ..

(+15m^2+20m-6m-8)=0

We get rid of parentheses

15m^2+20m-6m-8=0

We add all the numbers together, and all the variables

15m^2+14m-8=0

a = 15; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·15·(-8)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*15}=\frac{-40}{30}
=-1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*15}=\frac{12}{30}
=2/5
$