Calculate: -4y^2+6y=0

Expression: $-4{y}^{2}+6y=0$

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

$\begin{array} { l }a=-4,& b=6,& c=0\end{array}$

Substitute $a=-4$, $b=6$ and $c=0$ into the quadratic formula $y=\frac{ -b\pm\sqrt{ {b}^{2}-4ac } }{ 2a }$

$y=\frac{ -6\pm\sqrt{ {6}^{2}-4 \times \left( -4 \right) \times 0 } }{ 2 \times \left( -4 \right) }$

Any expression multiplied by $0$ equals $0$

$y=\frac{ -6\pm\sqrt{ {6}^{2}-0 } }{ 2 \times \left( -4 \right) }$

Multiply the numbers

$y=\frac{ -6\pm\sqrt{ {6}^{2}-0 } }{ -8 }$

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

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

Reduce the index of the radical and exponent with $2$

$y=\frac{ -6\pm6 }{ -8 }$

Use $\frac{ -a }{ b }=\frac{ a }{ -b }=-\frac{ a }{ b }$ to rewrite the fraction

$y=-\frac{ -6\pm6 }{ 8 }$

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

$\begin{array} { l }y=-\frac{ -6+6 }{ 8 },\\y=-\frac{ -6-6 }{ 8 }\end{array}$

Simplify the expression

$\begin{array} { l }y=0,\\y=-\frac{ -6-6 }{ 8 }\end{array}$

Simplify the expression

$\begin{array} { l }y=0,\\y=\frac{ 3 }{ 2 }\end{array}$

The equation has $2$ solutions

\begin{align*}&\begin{array} { l }y_1=0,& y_2=\frac{ 3 }{ 2 }\end{array} \\&\begin{array} { l }y_1=0,& y_2=1.5\end{array}\end{align*}

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