How do you use the quadratic formula to solve #-6x^2+3x+2=3#?

Question

2588 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-18T04:46:57

#(1+-isqrt15)/4#

The first thing we need to do before solving using the quadratic formula, is to get everything to one side, causing the equation to equal zero:

#-6x^2+3x+2=3 => -6x^2+3x-1=0#

Having this, we can now solve using the quadratic formula.

The quadratic formula is as follows:

#(-color(red)(b)+-sqrt(color(red)(b)^2-4color(orange)(a)color(blue)(c)))/(2color(orange)(a))#

We derive each of these values from the quadratic:

#color(orange)(a)x^2+color(red)(b)x+color(blue)(c)# so #" "color(orange)(a = -6" "color(red)(b = 3) " "color(blue)(c=-1)#

Now we plug in our corresponding numbers:

#(-3+-sqrt(3^2-4(-6)(-1)))/(2(-6)#

#=(-3+-sqrt(9-24))/-12#

#=(-3+-sqrt(-15))/-12#

#=(1+-isqrt15)/4#