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

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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:

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

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

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

$=(1+-isqrt15)/4$

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