Question

What are the roots of the equation?-3= -6x^2+7x

Answer 1

We have the next equation

`-3=-6x^2+7x`

First, we need to set the equation to zero

`6x^2-7x-3=0`

then we will use the general formula to find the roots of a second-degree equation

`x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where

a=6

b=-7

c=-3

then we substitute the values

`x_(1,2)=\frac{7\pm\sqrt[]{(-7)^2-4(6)(-3)}}{2(6)}`
`\begin{gathered} x_(1,2)=\frac{7\pm\sqrt[]{49^{}+72}}{12} \\ x_(1,2)=\frac{7\pm\sqrt[]{121}}{12} \\ x_(1,2)=(7\pm11)/(12) \\ \end{gathered}`
`x_1=(7+11)/(12)=(18)/(12)=(3)/(2)`

`x_2=(7-11)/(12)=(-4)/(12)=-(1)/(3)`

the roots of the equation are x=3/2, x=-1/3