7m(m-2)=3(2-m)

Solution for 7m(m-2)=3(2-m) equation:

7m(m-2)=3(2-m)

We move all terms to the left:

7m(m-2)-(3(2-m))=0

We add all the numbers together, and all the variables

7m(m-2)-(3(-1m+2))=0

We multiply parentheses

7m^2-14m-(3(-1m+2))=0


We calculate terms in parentheses: -(3(-1m+2)), so:

3(-1m+2)

We multiply parentheses

-3m+6

Back to the equation:

-(-3m+6)


We get rid of parentheses

7m^2-14m+3m-6=0

We add all the numbers together, and all the variables

7m^2-11m-6=0

a = 7; b = -11; c = -6;
Δ = b2-4ac
Δ = -112-4·7·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*7}=\frac{-6}{14}
=-3/7
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*7}=\frac{28}{14}
=2
$