5-(m-4)=2m+3m(m-1)

Solution for 5-(m-4)=2m+3m(m-1) equation:

5-(m-4)=2m+3m(m-1)

We move all terms to the left:

5-(m-4)-(2m+3m(m-1))=0

We get rid of parentheses

-m-(2m+3m(m-1))+4+5=0


We calculate terms in parentheses: -(2m+3m(m-1)), so:

2m+3m(m-1)

We multiply parentheses

3m^2+2m-3m

We add all the numbers together, and all the variables

3m^2-1m

Back to the equation:

-(3m^2-1m)


We add all the numbers together, and all the variables

-1m-(3m^2-1m)+9=0

We get rid of parentheses

-3m^2-1m+1m+9=0

We add all the numbers together, and all the variables

-3m^2+9=0

a = -3; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-3)·9
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-3}=\frac{0-6\sqrt{3}}{-6}
=-\frac{6\sqrt{3}}{-6}
=-\frac{\sqrt{3}}{-1}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-3}=\frac{0+6\sqrt{3}}{-6}
=\frac{6\sqrt{3}}{-6}
=\frac{\sqrt{3}}{-1}
$