12=4m(8m+10)

Solution for 12=4m(8m+10) equation:

12=4m(8m+10)

We move all terms to the left:

12-(4m(8m+10))=0


We calculate terms in parentheses: -(4m(8m+10)), so:

4m(8m+10)

We multiply parentheses

32m^2+40m

Back to the equation:

-(32m^2+40m)


We get rid of parentheses

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

a = -32; b = -40; c = +12;
Δ = b2-4ac
Δ = -402-4·(-32)·12
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-56}{2*-32}=\frac{-16}{-64}
=1/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+56}{2*-32}=\frac{96}{-64}
=-1+1/2
$