X2+11=10x

Solution for X2+11=10x equation:

X2+11=10X

We move all terms to the left:

X2+11-(10X)=0

We add all the numbers together, and all the variables

X^2-10X+11=0

a = 1; b = -10; c = +11;
Δ = b2-4ac
Δ = -102-4·1·11
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{14}}{2*1}=\frac{10-2\sqrt{14}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{14}}{2*1}=\frac{10+2\sqrt{14}}{2}
$