11-x^2=14x

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

11-x^2=14x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

a = -1; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·(-1)·11
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{15}}{2*-1}=\frac{14-4\sqrt{15}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{15}}{2*-1}=\frac{14+4\sqrt{15}}{-2}
$