14x+322=x^2

Solution for 14x+322=x^2 equation:

14x+322=x^2

We move all terms to the left:

14x+322-(x^2)=0

determiningTheFunctionDomain
-x^2+14x+322=0

We add all the numbers together, and all the variables

-1x^2+14x+322=0

a = -1; b = 14; c = +322;
Δ = b2-4ac
Δ = 142-4·(-1)·322
Δ = 1484
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:

$\sqrt{\Delta}=\sqrt{1484}=\sqrt{4*371}=\sqrt{4}*\sqrt{371}=2\sqrt{371}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{371}}{2*-1}=\frac{-14-2\sqrt{371}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{371}}{2*-1}=\frac{-14+2\sqrt{371}}{-2}
$