10(3m-1)(m+1)=6m-2

Solution for 10(3m-1)(m+1)=6m-2 equation:

10(3m-1)(m+1)=6m-2

We move all terms to the left:

10(3m-1)(m+1)-(6m-2)=0

We get rid of parentheses

10(3m-1)(m+1)-6m+2=0

We multiply parentheses ..

10(+3m^2+3m-1m-1)-6m+2=0

We multiply parentheses

30m^2+30m-10m-6m-10+2=0

We add all the numbers together, and all the variables

30m^2+14m-8=0

a = 30; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·30·(-8)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-34}{2*30}=\frac{-48}{60}
=-4/5
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+34}{2*30}=\frac{20}{60}
=1/3
$