3(m+1.5)=1.5(2m+3)m=

Solution for 3(m+1.5)=1.5(2m+3)m= equation:

3(m+1.5)=1.5(2m+3)m=

We move all terms to the left:

3(m+1.5)-(1.5(2m+3)m)=0

We multiply parentheses

3m-(1.5(2m+3)m)+4.5=0


We calculate terms in parentheses: -(1.5(2m+3)m), so:

1.5(2m+3)m

We multiply parentheses

2m^2+3m

Back to the equation:

-(2m^2+3m)


We get rid of parentheses

-2m^2+3m-3m+4.5=0

We add all the numbers together, and all the variables

-2m^2+4.5=0

a = -2; b = 0; c = +4.5;
Δ = b2-4ac
Δ = 02-4·(-2)·4.5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-2}=\frac{6}{-4}
=-1+1/2
$