How do you solve $3x^2 - 4x = 2$ using the quadratic formula?

Question

4816 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-27T13:43:10

$1.721$ and $-.387$

First you want to get all of the variable on the same side

$3x^2 - 4x = 2$

$3x^2 - 4x - 2 = 0$

Remember that $ax^2 + bx + c = 0$ so $a = 3$ , $b = -4$ , and $c = -2$

$x_(1,2) = (-b +- sqrt(b^2 - 4ac))/(2a)$

so

$x_(1,2) = ( -(-4) +- sqrt( (-4)^2 - 4(3)(-2)))/(2(3))$

$x_(1,2) = ( 4 +- sqrt( 16 + 24 ) ) / 6$

$x_(1,2) = ( 4 +- sqrt( 40 ) ) / 6$

Since $sqrt 40 = 6.325$ (rounded), sub that in and add/subtract according to the equation

$(4 + 6.325) / 6 = 1.721$

$(4 - 6.325) / 6 = - .387$

How do you solve 3x^2 - 4x = 23x^2 - 4x = 2 using the quadratic formula?