8-2m(m+7)=5m-12

Solution for 8-2m(m+7)=5m-12 equation:

8-2m(m+7)=5m-12

We move all terms to the left:

8-2m(m+7)-(5m-12)=0

We multiply parentheses

-2m^2-14m-(5m-12)+8=0

We get rid of parentheses

-2m^2-14m-5m+12+8=0

We add all the numbers together, and all the variables

-2m^2-19m+20=0

a = -2; b = -19; c = +20;
Δ = b2-4ac
Δ = -192-4·(-2)·20
Δ = 521
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{-(-19)-\sqrt{521}}{2*-2}=\frac{19-\sqrt{521}}{-4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{521}}{2*-2}=\frac{19+\sqrt{521}}{-4}
$