0=2x^2-14x+9

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

0=2x^2-14x+9

We move all terms to the left:

0-(2x^2-14x+9)=0

We add all the numbers together, and all the variables

-(2x^2-14x+9)=0

We get rid of parentheses

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

The end solution:

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