$2{x}^{2}+8x=\left( x-3 \right) \times \left( x-3 \right)$
The factor $x-3$ repeats $2$ times, so the base is $x-3$ and the exponent is $2$$2{x}^{2}+8x={\left( x-3 \right)}^{2}$
Use ${\left( a-b \right)}^{2}={a}^{2}-2ab+{b}^{2}$ to expand the expression$2{x}^{2}+8x={x}^{2}-6x+9$
Move the expression to the left-hand side and change its sign$2{x}^{2}+8x-{x}^{2}+6x-9=0$
Collect like terms${x}^{2}+8x+6x-9=0$
Collect like terms${x}^{2}+14x-9=0$
Identify the coefficients $a$, $b$ and $c$ of the quadratic equation$\begin{array} { l }a=1,& b=14,& c=-9\end{array}$
Substitute $a=1$, $b=14$ and $c=-9$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times 1 \times \left( -9 \right) } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times \left( -9 \right) } }{ 2 \times 1 }$
Any expression multiplied by $1$ remains the same$x=\frac{ -14\pm\sqrt{ {14}^{2}-4 \times \left( -9 \right) } }{ 2 }$
Evaluate the power$x=\frac{ -14\pm\sqrt{ 196-4 \times \left( -9 \right) } }{ 2 }$
Multiply the numbers$x=\frac{ -14\pm\sqrt{ 196+36 } }{ 2 }$
Add the numbers$x=\frac{ -14\pm\sqrt{ 232 } }{ 2 }$
Simplify the radical expression$x=\frac{ -14\pm2\sqrt{ 58 } }{ 2 }$
Write the solutions, one with a $+$ sign and one with a $-$ sign$\begin{array} { l }x=\frac{ -14+2\sqrt{ 58 } }{ 2 },\\x=\frac{ -14-2\sqrt{ 58 } }{ 2 }\end{array}$
Simplify the expression$\begin{array} { l }x=-7+\sqrt{ 58 },\\x=\frac{ -14-2\sqrt{ 58 } }{ 2 }\end{array}$
Simplify the expression$\begin{array} { l }x=-7+\sqrt{ 58 },\\x=-7-\sqrt{ 58 }\end{array}$
The equation has $2$ solutions$\begin{align*}&\begin{array} { l }x_1=-7-\sqrt{ 58 },& x_2=-7+\sqrt{ 58 }\end{array} \\&\begin{array} { l }x_1\approx-14.61577,& x_2\approx0.615773\end{array}\end{align*}$