-5m(m-5)=4(m+1)

Solution for -5m(m-5)=4(m+1) equation:

-5m(m-5)=4(m+1)

We move all terms to the left:

-5m(m-5)-(4(m+1))=0

We multiply parentheses

-5m^2+25m-(4(m+1))=0


We calculate terms in parentheses: -(4(m+1)), so:

4(m+1)

We multiply parentheses

4m+4

Back to the equation:

-(4m+4)


We get rid of parentheses

-5m^2+25m-4m-4=0

We add all the numbers together, and all the variables

-5m^2+21m-4=0

a = -5; b = 21; c = -4;
Δ = b2-4ac
Δ = 212-4·(-5)·(-4)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-19}{2*-5}=\frac{-40}{-10}
=+4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+19}{2*-5}=\frac{-2}{-10}
=1/5
$