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

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

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

We multiply parentheses ..

5(+8m^2-6m+12m-9)=0

We multiply parentheses

40m^2-30m+60m-45=0

We add all the numbers together, and all the variables

40m^2+30m-45=0

a = 40; b = 30; c = -45;
Δ = b2-4ac
Δ = 302-4·40·(-45)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-90}{2*40}=\frac{-120}{80}
=-1+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+90}{2*40}=\frac{60}{80}
=3/4
$