Evaluate: 2x^2+7x-9=0

Expression: $2{x}^{2}+7x-9=0$

Write $7x$ as a difference

$2{x}^{2}+9x-2x-9=0$

Factor out $x$ from the expression

$x \times \left( 2x+9 \right)-2x-9=0$

Factor out the negative sign from the expression

$x \times \left( 2x+9 \right)-\left( 2x+9 \right)=0$

Factor out $2x+9$ from the expression

$\left( 2x+9 \right) \times \left( x-1 \right)=0$

When the product of factors equals $0$, at least one factor is $0$

$\begin{array} { l }2x+9=0,\\x-1=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-\frac{ 9 }{ 2 },\\x-1=0\end{array}$

Solve the equation for $x$

$\begin{array} { l }x=-\frac{ 9 }{ 2 },\\x=1\end{array}$

The equation has $2$ solutions

$\begin{align*}&\begin{array} { l }x_1=-\frac{ 9 }{ 2 },& x_2=1\end{array} \\&\begin{array} { l }x_1=-4.5,& x_2=1\end{array}\end{align*}$