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

$x_2=\frac{7-11}{12}=\frac{-4}{12}=-\frac{1}{3}$

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