2-(13-m)=-1m(m-19)-16

Solution for 2-(13-m)=-1m(m-19)-16 equation:

2-(13-m)=-1m(m-19)-16

We move all terms to the left:

2-(13-m)-(-1m(m-19)-16)=0

We add all the numbers together, and all the variables

-(-1m+13)-(-1m(m-19)-16)+2=0

We get rid of parentheses

1m-(-1m(m-19)-16)-13+2=0


We calculate terms in parentheses: -(-1m(m-19)-16), so:

-1m(m-19)-16

We multiply parentheses

-m^2+19m-16

We add all the numbers together, and all the variables

-1m^2+19m-16

Back to the equation:

-(-1m^2+19m-16)


We add all the numbers together, and all the variables

-(-1m^2+19m-16)+m-11=0

We get rid of parentheses

1m^2-19m+m+16-11=0

We add all the numbers together, and all the variables

m^2-18m+5=0

a = 1; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·1·5
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{19}}{2*1}=\frac{18-4\sqrt{19}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{19}}{2*1}=\frac{18+4\sqrt{19}}{2}
$