$5u+14={u}^{2}$
Move the variable to the left-hand side and change its sign$5u+14-{u}^{2}=0$
Use the commutative property to reorder the terms$-{u}^{2}+5u+14=0$
Change the signs on both sides of the equation${u}^{2}-5u-14=0$
Write $-5u$ as a difference${u}^{2}+2u-7u-14=0$
Factor out $u$ from the expression$u \times \left( u+2 \right)-7u-14=0$
Factor out $-7$ from the expression$u \times \left( u+2 \right)-7\left( u+2 \right)=0$
Factor out $u+2$ from the expression$\left( u+2 \right) \times \left( u-7 \right)=0$
When the product of factors equals $0$, at least one factor is $0$$\begin{array} { l }u+2=0,\\u-7=0\end{array}$
Solve the equation for $u$$\begin{array} { l }u=-2,\\u-7=0\end{array}$
Solve the equation for $u$$\begin{array} { l }u=-2,\\u=7\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }\sqrt{ 5 \times \left( -2 \right)+14 }=-2,\\u=7\end{array}$
Check if the given value is the solution of the equation$\begin{array} { l }\sqrt{ 5 \times \left( -2 \right)+14 }=-2,\\\sqrt{ 5 \times 7+14 }=7\end{array}$
Simplify the expression$\begin{array} { l }2=-2,\\\sqrt{ 5 \times 7+14 }=7\end{array}$
Simplify the expression$\begin{array} { l }2=-2,\\7=7\end{array}$
The equality is false, therefore $u=-2$ is not a solution of the equation$\begin{array} { l }u≠-2,\\7=7\end{array}$
The equality is true, therefore $u=7$ is a solution of the equation$\begin{array} { l }u≠-2,\\u=7\end{array}$
The equation has one solution$u=7$