(3m+8)(5m-4)=0

Solution for (3m+8)(5m-4)=0 equation:

(3m+8)(5m-4)=0

We multiply parentheses ..

(+15m^2-12m+40m-32)=0

We get rid of parentheses

15m^2-12m+40m-32=0

We add all the numbers together, and all the variables

15m^2+28m-32=0

a = 15; b = 28; c = -32;
Δ = b2-4ac
Δ = 282-4·15·(-32)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-52}{2*15}=\frac{-80}{30}
=-2+2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+52}{2*15}=\frac{24}{30}
=4/5
$