0=x^2-11x+14

Solution for 0=x^2-11x+14 equation:

0=x^2-11x+14

We move all terms to the left:

0-(x^2-11x+14)=0

We add all the numbers together, and all the variables

-(x^2-11x+14)=0

We get rid of parentheses

-x^2+11x-14=0

We add all the numbers together, and all the variables

-1x^2+11x-14=0

a = -1; b = 11; c = -14;
Δ = b2-4ac
Δ = 112-4·(-1)·(-14)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{65}}{2*-1}=\frac{-11-\sqrt{65}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{65}}{2*-1}=\frac{-11+\sqrt{65}}{-2}
$