2m^2-22m-53=0

Solution for 2m^2-22m-53=0 equation:

2m^2-22m-53=0

a = 2; b = -22; c = -53;
Δ = b2-4ac
Δ = -222-4·2·(-53)
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{227}}{2*2}=\frac{22-2\sqrt{227}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{227}}{2*2}=\frac{22+2\sqrt{227}}{4}
$