Solve for: -5w^2+180=0

Expression: $-5{w}^{2}+180=0$

Divide both sides of the equation by $-5$

${w}^{2}-36=0$

Identify the coefficients $p$ and $q$ of the quadratic equation

$\begin{array} { l }p=0,& q=-36\end{array}$

Substitute $p=0$ and $q=-36$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$

$w=-\frac{ 0 }{ 2 }\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -36 \right) }$

$0$ divided by any non-zero expression equals $0$

$w=-0\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -36 \right) }$

Simplify the expression

$w=-0\pm6$

Removing $0$ doesn't change the value, so remove it from the expression

$w=6$

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

$\begin{array} { l }w=6,\\w=-6\end{array}$

The equation has $2$ solutions

$\begin{array} { l }w_1=-6,& w_2=6\end{array}$