$x-36-{x}^{2}+11x=0$
Collect like terms$12x-36-{x}^{2}=0$
Use the commutative property to reorder the terms$-{x}^{2}+12x-36=0$
Change the signs on both sides of the equation${x}^{2}-12x+36=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=1,& b=-12,& c=36\end{array}$
Substitute $a=1$, $b=-12$ and $c=36$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 1 \times 36 } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -\left( -12 \right)\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 }$
When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses$x=\frac{ 12\pm\sqrt{ {\left( -12 \right)}^{2}-4 \times 36 } }{ 2 }$
Evaluate the power$x=\frac{ 12\pm\sqrt{ 144-4 \times 36 } }{ 2 }$
Multiply the numbers$x=\frac{ 12\pm\sqrt{ 144-144 } }{ 2 }$
The sum of two opposites equals $0$$x=\frac{ 12\pm\sqrt{ 0 } }{ 2 }$
Any root of $0$ equals $0$$x=\frac{ 12\pm0 }{ 2 }$
Removing $0$ doesn't change the value, so remove it from the expression$x=\frac{ 12 }{ 2 }$
Cancel out the common factor $2$$x=6$