m(6m+3)=2(9m-4)

Solution for m(6m+3)=2(9m-4) equation:

m(6m+3)=2(9m-4)

We move all terms to the left:

m(6m+3)-(2(9m-4))=0

We multiply parentheses

6m^2+3m-(2(9m-4))=0


We calculate terms in parentheses: -(2(9m-4)), so:

2(9m-4)

We multiply parentheses

18m-8

Back to the equation:

-(18m-8)


We get rid of parentheses

6m^2+3m-18m+8=0

We add all the numbers together, and all the variables

6m^2-15m+8=0

a = 6; b = -15; c = +8;
Δ = b2-4ac
Δ = -152-4·6·8
Δ = 33
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{-(-15)-\sqrt{33}}{2*6}=\frac{15-\sqrt{33}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{33}}{2*6}=\frac{15+\sqrt{33}}{12}
$