6m(m-1)=3(3m+5)

Solution for 6m(m-1)=3(3m+5) equation:

6m(m-1)=3(3m+5)

We move all terms to the left:

6m(m-1)-(3(3m+5))=0

We multiply parentheses

6m^2-6m-(3(3m+5))=0


We calculate terms in parentheses: -(3(3m+5)), so:

3(3m+5)

We multiply parentheses

9m+15

Back to the equation:

-(9m+15)


We get rid of parentheses

6m^2-6m-9m-15=0

We add all the numbers together, and all the variables

6m^2-15m-15=0

a = 6; b = -15; c = -15;
Δ = b2-4ac
Δ = -152-4·6·(-15)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{65}}{2*6}=\frac{15-3\sqrt{65}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{65}}{2*6}=\frac{15+3\sqrt{65}}{12}
$