3m(m+5)=10m+1

Solution for 3m(m+5)=10m+1 equation:

3m(m+5)=10m+1

We move all terms to the left:

3m(m+5)-(10m+1)=0

We multiply parentheses

3m^2+15m-(10m+1)=0

We get rid of parentheses

3m^2+15m-10m-1=0

We add all the numbers together, and all the variables

3m^2+5m-1=0

a = 3; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·3·(-1)
Δ = 37
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{-(5)-\sqrt{37}}{2*3}=\frac{-5-\sqrt{37}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{37}}{2*3}=\frac{-5+\sqrt{37}}{6}
$