38m(m+5)=38m-20

Solution for 38m(m+5)=38m-20 equation:

38m(m+5)=38m-20

We move all terms to the left:

38m(m+5)-(38m-20)=0

We multiply parentheses

38m^2+190m-(38m-20)=0

We get rid of parentheses

38m^2+190m-38m+20=0

We add all the numbers together, and all the variables

38m^2+152m+20=0

a = 38; b = 152; c = +20;
Δ = b2-4ac
Δ = 1522-4·38·20
Δ = 20064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20064}=\sqrt{16*1254}=\sqrt{16}*\sqrt{1254}=4\sqrt{1254}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(152)-4\sqrt{1254}}{2*38}=\frac{-152-4\sqrt{1254}}{76}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(152)+4\sqrt{1254}}{2*38}=\frac{-152+4\sqrt{1254}}{76}
$