15+6(m+3)=2m(m+3)

Solution for 15+6(m+3)=2m(m+3) equation:

15+6(m+3)=2m(m+3)

We move all terms to the left:

15+6(m+3)-(2m(m+3))=0

We multiply parentheses

6m-(2m(m+3))+18+15=0


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

2m(m+3)

We multiply parentheses

2m^2+6m

Back to the equation:

-(2m^2+6m)


We add all the numbers together, and all the variables

6m-(2m^2+6m)+33=0

We get rid of parentheses

-2m^2+6m-6m+33=0

We add all the numbers together, and all the variables

-2m^2+33=0

a = -2; b = 0; c = +33;
Δ = b2-4ac
Δ = 02-4·(-2)·33
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{66}}{2*-2}=\frac{0-2\sqrt{66}}{-4}
=-\frac{2\sqrt{66}}{-4}
=-\frac{\sqrt{66}}{-2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{66}}{2*-2}=\frac{0+2\sqrt{66}}{-4}
=\frac{2\sqrt{66}}{-4}
=\frac{\sqrt{66}}{-2}
$