How do you solve -3x^2=2(3x-5)−3x2=2(3x−5) using the quadratic formula?

1 Answer
JJ The Pyro .
Jan 22, 2017

Rearrange to form: 3x^2+6x-10=03x2+6x−10=0
Substitute in quadratic formula: x=(-(6)+-sqrt((6)^2-4(3)(-10)))/(2(3))x=−(6)±√(6)2−4(3)(−10)2(3)
Simplify to get: x=(-3+sqrt(39))/(3) ~~1.08167x=−3+√393≈1.08167 or x=(-3-sqrt(39))/(3)~~-3.08167x=−3−√393≈−3.08167

Explanation:

First of all you need to rearrange the equation into the form ax^2+bx+c=0ax2+bx+c=0

So first expand the brackets on the right hand side: -3x^2=6x-10−3x2=6x−10

Then you can either take the -3x^2−3x2 over or the 6x-106x−10 over.

Let's just take the -3x^2−3x2 over to give: 3x^2+6x-10=03x2+6x−10=0

Now we can see what aa bb and cc are:
a=3a=3
b=6b=6
c=-10c=−10

Then we substitute these into the quadratic formula:
x=(-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a
Quadratics usually have 2 answers which is why there is a +-± as for one answer you use ++ and the other -−.

So now substituting in: x=(-(6)+-sqrt((6)^2-4(3)(-10)))/(2(3))x=−(6)±√(6)2−4(3)(−10)2(3)

This simplifies to: x=(-6+-2sqrt(39))/(6)x=−6±2√396

And dividing all terms by 2 to: x=(-3+-sqrt(39))/(3)x=−3±√393 which is the most simple form.

So x=(-3+sqrt(39))/(3) ~~1.08167x=−3+√393≈1.08167 or x=(-3-sqrt(39))/(3)~~-3.08167x=−3−√393≈−3.08167

Related questions
See all questions in Quadratic Formula
Impact of this question
2006 views around the world
You can reuse this answer
Creative Commons License