2m^2-14m+9=0

Solution for 2m^2-14m+9=0 equation:

2m^2-14m+9=0

a = 2; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·2·9
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{31}}{2*2}=\frac{14-2\sqrt{31}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{31}}{2*2}=\frac{14+2\sqrt{31}}{4}
$