6m(m+5)=19m-4

Solution for 6m(m+5)=19m-4 equation:

6m(m+5)=19m-4

We move all terms to the left:

6m(m+5)-(19m-4)=0

We multiply parentheses

6m^2+30m-(19m-4)=0

We get rid of parentheses

6m^2+30m-19m+4=0

We add all the numbers together, and all the variables

6m^2+11m+4=0

a = 6; b = 11; c = +4;
Δ = b2-4ac
Δ = 112-4·6·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*6}=\frac{-16}{12}
=-1+1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*6}=\frac{-6}{12}
=-1/2
$