m^2=-12m+83

Solution for m^2=-12m+83 equation:

m^2=-12m+83

We move all terms to the left:

m^2-(-12m+83)=0

We get rid of parentheses

m^2+12m-83=0

a = 1; b = 12; c = -83;
Δ = b2-4ac
Δ = 122-4·1·(-83)
Δ = 476
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:

$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{119}}{2*1}=\frac{-12-2\sqrt{119}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{119}}{2*1}=\frac{-12+2\sqrt{119}}{2}
$