Question

Solve for x algebraically. No decimal solutions and reduce if possible. 6x^2=20x

Answer 1

`\bf 6x^2=20x\implies 60xx=20x\implies 60x=\cfrac{20~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 60x = 20`

`\bf x = \cfrac{20}{60}\implies x = \cfrac{~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot ~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2\cdot 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 3\cdot ~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies x = \cfrac{1}{3}`