${x}^{2}+6x-4x-24=11$
Collect like terms${x}^{2}+2x-24=11$
Move the constant to the left-hand side and change its sign${x}^{2}+2x-24-11=0$
Calculate the difference${x}^{2}+2x-35=0$
Identify the coefficients $p$ and $q$ of the quadratic equation$\begin{array} { l }p=2,& q=-35\end{array}$
Substitute $p=2$ and $q=-35$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$$x=-\frac{ 2 }{ 2 }\pm\sqrt{ {\left( \frac{ 2 }{ 2 } \right)}^{2}-\left( -35 \right) }$
Any expression divided by itself equals $1$$x=-1\pm\sqrt{ {\left( \frac{ 2 }{ 2 } \right)}^{2}-\left( -35 \right) }$
Simplify the expression$x=-1\pm6$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }x=-1+6,\\x=-1-6\end{array}$
Calculate the sum$\begin{array} { l }x=5,\\x=-1-6\end{array}$
Calculate the difference$\begin{array} { l }x=5,\\x=-7\end{array}$
The equation has $2$ solutions$\begin{array} { l }x_1=-7,& x_2=5\end{array}$