m^2+3m=53

Solution for m^2+3m=53 equation:

m^2+3m=53

We move all terms to the left:

m^2+3m-(53)=0

a = 1; b = 3; c = -53;
Δ = b2-4ac
Δ = 32-4·1·(-53)
Δ = 221
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{221}}{2*1}=\frac{-3-\sqrt{221}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{221}}{2*1}=\frac{-3+\sqrt{221}}{2}
$