m^2-14m=23

Solution for m^2-14m=23 equation:

m^2-14m=23

We move all terms to the left:

m^2-14m-(23)=0

a = 1; b = -14; c = -23;
Δ = b2-4ac
Δ = -142-4·1·(-23)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-12\sqrt{2}}{2*1}=\frac{14-12\sqrt{2}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+12\sqrt{2}}{2*1}=\frac{14+12\sqrt{2}}{2}
$