0.5(m+4)=3m(m-1)

Solution for 0.5(m+4)=3m(m-1) equation:

0.5(m+4)=3m(m-1)

We move all terms to the left:

0.5(m+4)-(3m(m-1))=0

We multiply parentheses

0.5m-(3m(m-1))+2=0


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

3m(m-1)

We multiply parentheses

3m^2-3m

Back to the equation:

-(3m^2-3m)


We get rid of parentheses

-3m^2+0.5m+3m+2=0

We add all the numbers together, and all the variables

-3m^2+3.5m+2=0

a = -3; b = 3.5; c = +2;
Δ = b2-4ac
Δ = 3.52-4·(-3)·2
Δ = 36.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3.5)-\sqrt{36.25}}{2*-3}=\frac{-3.5-\sqrt{36.25}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3.5)+\sqrt{36.25}}{2*-3}=\frac{-3.5+\sqrt{36.25}}{-6}
$