# Calculate: 4y^2-3=13

## Expression: $4{y}^{2}-3=13$

Move the constant to the left-hand side and change its sign

$4{y}^{2}-3-13=0$

Calculate the difference

$4{y}^{2}-16=0$

Divide both sides of the equation by $4$

${y}^{2}-4=0$

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

$\begin{array} { l }p=0,& q=-4\end{array}$

Substitute $p=0$ and $q=-4$ into the PQ formula $x=-\frac{ p }{ 2 }\pm\sqrt{ {\left( \frac{ p }{ 2 } \right)}^{2}-q }$

$y=-\frac{ 0 }{ 2 }\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -4 \right) }$

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

$y=-0\pm\sqrt{ {\left( \frac{ 0 }{ 2 } \right)}^{2}-\left( -4 \right) }$

Simplify the expression

$y=-0\pm2$

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

$y=2$

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

$\begin{array} { l }y=2,\\y=-2\end{array}$

The equation has $2$ solutions

$\begin{array} { l }y_1=-2,& y_2=2\end{array}$

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