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

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

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

We move all terms to the left:

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

We use the square of the difference formula

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


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

5m(m+3)-3

We multiply parentheses

5m^2+15m-3

Back to the equation:

-(5m^2+15m-3)


We get rid of parentheses

-5m^2+3m-15m+3=0

We add all the numbers together, and all the variables

-5m^2-12m+3=0

a = -5; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·(-5)·3
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*-5}=\frac{12-2\sqrt{51}}{-10}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*-5}=\frac{12+2\sqrt{51}}{-10}
$