2m^2-31m=m-78

Solution for 2m^2-31m=m-78 equation:

2m^2-31m=m-78

We move all terms to the left:

2m^2-31m-(m-78)=0

We get rid of parentheses

2m^2-31m-m+78=0

We add all the numbers together, and all the variables

2m^2-32m+78=0

a = 2; b = -32; c = +78;
Δ = b2-4ac
Δ = -322-4·2·78
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-20}{2*2}=\frac{12}{4}
=3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+20}{2*2}=\frac{52}{4}
=13
$