6x=x^2-4x+11

Solution for 6x=x^2-4x+11 equation:

6x=x^2-4x+11

We move all terms to the left:

6x-(x^2-4x+11)=0

We get rid of parentheses

-x^2+6x+4x-11=0

We add all the numbers together, and all the variables

-1x^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}
$