x^2=14x-11=0

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

x^2=14x-11=0

We move all terms to the left:

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

We get rid of parentheses

x^2-14x+11=0

a = 1; b = -14; c = +11;
Δ = b2-4ac
Δ = -142-4·1·11
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{38}}{2*1}=\frac{14-2\sqrt{38}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{38}}{2*1}=\frac{14+2\sqrt{38}}{2}
$