7m-2m(m-3)=3m-14

Solution for 7m-2m(m-3)=3m-14 equation:

7m-2m(m-3)=3m-14

We move all terms to the left:

7m-2m(m-3)-(3m-14)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2m^2+10m+14=0

a = -2; b = 10; c = +14;
Δ = b2-4ac
Δ = 102-4·(-2)·14
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{53}}{2*-2}=\frac{-10-2\sqrt{53}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{53}}{2*-2}=\frac{-10+2\sqrt{53}}{-4}
$