1m^2+22m=-23

Solution for 1m^2+22m=-23 equation:

1m^2+22m=-23

We move all terms to the left:

1m^2+22m-(-23)=0

We add all the numbers together, and all the variables

m^2+22m+23=0

a = 1; b = 22; c = +23;
Δ = b2-4ac
Δ = 222-4·1·23
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-14\sqrt{2}}{2*1}=\frac{-22-14\sqrt{2}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+14\sqrt{2}}{2*1}=\frac{-22+14\sqrt{2}}{2}
$