How do you solve 10x^2=-7x+6 using the quadratic formula?

1 Answer
Mar 11, 2018

x = 1/2 or x = -6/5

Explanation:

The quadratic formula allows us to find the value of x for an equation in the form ax^2 + bx + c = 0 where a ne 0. In the case that the equation is in this form:

x = (-color(green)b +- sqrt(color(green)b^2 - 4color(red)acolor(blue)c))/(2color(red)a)

The first thing we notice is that this equation is not in that form, so we should rearrange the terms so it is.

10x^2 = -7x + 6

color(red)10x^2 + color(green)7x color(blue)(- 6) = 0

Now, we can substitute our coefficients into the quadratic formula. I recommend using parentheses around each coefficient to help ensure all of the signs are correct in our final answer.

x = (-(color(green)7) +- sqrt((color(green)7)^2 - 4(color(red)10)(color(blue)(-6))))/(2(color(red)10))

x = (-7 +- sqrt(289))/20

x = (-7 +- 17)/20

x = (-7 + 17)/20 or x = (-7 - 17)/20

x = 10/20 or x = (-24)/20

x = 1/2 or x = -6/5