Question

How do you solve `3x^2+7x-13=0`?

Answer 1

`color(blue)x=color(blue)((-7 +sqrt(205))/6` and `color(green)(x=(-7 -sqrt(205))/6`

Explanation:

This is a quadratic equation with respect to `x`. We will use the quadratic formula:

For an equation of the type
`color(purple)(ax^2 + bx + c = 0, color(red)(a!=0)`

`x=-b pmsqrt(b^2 -4ac)/(2a)`
Putting our values in the equation:

`x= -7 pmsqrt((7)^2-4(3)(-13))/(2(3))`
`x= -7pmsqrt(49+156)/6`

`=>` `color(magenta)(x=color(magenta)((-7 pmsqrt(205))/6`