Evaluate: x^2-5x+6=0

Expression: ${x}^{2}-5x+6=0$

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

$\begin{array} { l }a=1,& b=-5,& c=6\end{array}$

Substitute $a=1$, $b=-5$ and $c=6$ into the quadratic formula $x=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$x=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 1 \times 6 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 6 } }{ 2 \times 1 }$

Any expression multiplied by $1$ remains the same

$x=\frac{ -\left( -5 \right)\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 6 } }{ 2 }$

When there is a $-$ in front of an expression in parentheses, change the sign of each term of the expression and remove the parentheses

$x=\frac{ 5\pm\sqrt{ {\left( -5 \right)}^{2}-4 \times 6 } }{ 2 }$

Evaluate the power

$x=\frac{ 5\pm\sqrt{ 25-4 \times 6 } }{ 2 }$

Multiply the numbers

$x=\frac{ 5\pm\sqrt{ 25-24 } }{ 2 }$

Subtract the numbers

$x=\frac{ 5\pm\sqrt{ 1 } }{ 2 }$

Any root of $1$ equals $1$

$x=\frac{ 5\pm1 }{ 2 }$

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

$\begin{array} { l }x=\frac{ 5+1 }{ 2 },\\x=\frac{ 5-1 }{ 2 }\end{array}$

Simplify the expression

$\begin{array} { l }x=3,\\x=\frac{ 5-1 }{ 2 }\end{array}$

Simplify the expression

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

The equation has $2$ solutions

$\begin{array} { l }x_1=2,& x_2=3\end{array}$