10m-7-5+2-3m(m=8)

Solution for 10m-7-5+2-3m(m=8) equation:

10m-7-5+2-3m(m=8)

We move all terms to the left:

10m-7-5+2-3m(m-(8))=0

We add all the numbers together, and all the variables

10m-3m(m-8)-10=0

We multiply parentheses

-3m^2+10m+24m-10=0

We add all the numbers together, and all the variables

-3m^2+34m-10=0

a = -3; b = 34; c = -10;
Δ = b2-4ac
Δ = 342-4·(-3)·(-10)
Δ = 1036
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:

$\sqrt{\Delta}=\sqrt{1036}=\sqrt{4*259}=\sqrt{4}*\sqrt{259}=2\sqrt{259}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{259}}{2*-3}=\frac{-34-2\sqrt{259}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{259}}{2*-3}=\frac{-34+2\sqrt{259}}{-6}
$