10m(m+3)=2m-5

Solution for 10m(m+3)=2m-5 equation:

10m(m+3)=2m-5

We move all terms to the left:

10m(m+3)-(2m-5)=0

We multiply parentheses

10m^2+30m-(2m-5)=0

We get rid of parentheses

10m^2+30m-2m+5=0

We add all the numbers together, and all the variables

10m^2+28m+5=0

a = 10; b = 28; c = +5;
Δ = b2-4ac
Δ = 282-4·10·5
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-2\sqrt{146}}{2*10}=\frac{-28-2\sqrt{146}}{20}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{146}}{2*10}=\frac{-28+2\sqrt{146}}{20}
$