Evaluate: { ext{begin}array l-3=3y-(3)/(4)x } 3x=2y-8 ext{end}array .

Expression: ${x}^{2}+6x+7=0$

Identify the coefficients $a$, $b$ and $c$ of the quadratic equation

$\begin{array} { l }a=1,& b=6,& c=7\end{array}$

Substitute $a=1$, $b=6$ and $c=7$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -6\pm\sqrt{ {6}^{2}-4 \times 1 \times 7 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -6\pm\sqrt{ {6}^{2}-4 \times 7 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -6\pm\sqrt{ {6}^{2}-4 \times 7 } }{ 2 }$

Evaluate the power

$x=\frac{ -6\pm\sqrt{ 36-4 \times 7 } }{ 2 }$

Multiply the numbers

$x=\frac{ -6\pm\sqrt{ 36-28 } }{ 2 }$

Subtract the numbers

$x=\frac{ -6\pm\sqrt{ 8 } }{ 2 }$

Simplify the radical expression

$x=\frac{ -6\pm2\sqrt{ 2 } }{ 2 }$

Write the solutions, one with a $+$ sign and one with a $-$ sign

$\begin{array} { l }x=\frac{ -6+2\sqrt{ 2 } }{ 2 },\\x=\frac{ -6-2\sqrt{ 2 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=-3+\sqrt{ 2 },\\x=\frac{ -6-2\sqrt{ 2 } }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=-3+\sqrt{ 2 },\\x=-3-\sqrt{ 2 }\end{array}$

The equation has $2$ solutions

$\begin{align*}&\begin{array} { l }x_1=-3-\sqrt{ 2 },& x_2=-3+\sqrt{ 2 }\end{array} \\&\begin{array} { l }x_1\approx-4.41421,& x_2\approx-1.58579\end{array}\end{align*}$