Question

Solve the equation 6x^2-2x-3=0 and express the answer in simplest radical form

Answer 1

x=1+√19/6 or x=1-√19/6 (I put or because its both answers, you get plus/minus)

Answer 2

Solution:

we have been asked to solve the given equation

$6x^2-2x-3=0$

Compare this with the standard for of the quadratic equation.

$ax^2+bx+c=0$

we get $a=6, b=-2,c=-3$

As we know the roots is given using the formula

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} , b^2-4ac\geq 0, a\neq0$

Here we have

$\sqrt{b^2-4ac}= \sqrt{(-2)^2-4*6*(-3)}=\sqrt{76}=2\sqrt{19}$

$x=\frac{2\pm2\sqrt{19}}{12} =\frac{1}{6}\pm \frac{1}{6}\sqrt{19}\\ \\ \Rightarrow x =\frac{1}{6}+ \frac{1}{6}\sqrt{19},\frac{1}{6}- \frac{1}{6}\sqrt{19}$