m^2-10m-72=-7

Solution for m^2-10m-72=-7 equation:

m^2-10m-72=-7

We move all terms to the left:

m^2-10m-72-(-7)=0

We add all the numbers together, and all the variables

m^2-10m-65=0

a = 1; b = -10; c = -65;
Δ = b2-4ac
Δ = -102-4·1·(-65)
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{10}}{2*1}=\frac{10-6\sqrt{10}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{10}}{2*1}=\frac{10+6\sqrt{10}}{2}
$