2m^2-51=22m+1

Solution for 2m^2-51=22m+1 equation:

2m^2-51=22m+1

We move all terms to the left:

2m^2-51-(22m+1)=0

We get rid of parentheses

2m^2-22m-1-51=0

We add all the numbers together, and all the variables

2m^2-22m-52=0

a = 2; b = -22; c = -52;
Δ = b2-4ac
Δ = -222-4·2·(-52)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-30}{2*2}=\frac{-8}{4}
=-2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+30}{2*2}=\frac{52}{4}
=13
$