2c^2-14c+9=0

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

2c^2-14c+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:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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