Question

How do you solve `3y^2+5y-4=0` using the quadratic formula?

Answer 1

The solutions are `y = (-5+sqrt(73))/6 , y = (-5-sqrt(73))/6`

Explanation:

`3y^2 + 5y - 4 = 0`

The equation is of the form `color(blue)(ay^2+by+c=0` where:

`a=3, b=5, c= -4`

The Discriminant is given by:

`Delta=b^2-4*a*c`

`= (5)^2-(4* 3 * (-4))`

`= 25 + 48 = 73`

The solutions are found using the formula
`y=(-b+-sqrtDelta)/(2*a)`

`y = ((-5)+-sqrt(73))/(2*3) = (-5+-sqrt(73))/6`

The solutions are:

• `color(green)(y = (-5+sqrt(73))/6`

• `color(green)(y = (-5-sqrt(73))/6`