2(m-2)+6=4(m-1)13m

Solution for 2(m-2)+6=4(m-1)13m equation:

2(m-2)+6=4(m-1)13m

We move all terms to the left:

2(m-2)+6-(4(m-1)13m)=0

We multiply parentheses

2m-(4(m-1)13m)-4+6=0


We calculate terms in parentheses: -(4(m-1)13m), so:

4(m-1)13m

We multiply parentheses

52m^2-52m

Back to the equation:

-(52m^2-52m)


We add all the numbers together, and all the variables

2m-(52m^2-52m)+2=0

We get rid of parentheses

-52m^2+2m+52m+2=0

We add all the numbers together, and all the variables

-52m^2+54m+2=0

a = -52; b = 54; c = +2;
Δ = b2-4ac
Δ = 542-4·(-52)·2
Δ = 3332
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:

$\sqrt{\Delta}=\sqrt{3332}=\sqrt{196*17}=\sqrt{196}*\sqrt{17}=14\sqrt{17}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-14\sqrt{17}}{2*-52}=\frac{-54-14\sqrt{17}}{-104}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+14\sqrt{17}}{2*-52}=\frac{-54+14\sqrt{17}}{-104}
$