How do you solve #3x^2 – 2x = 15x – 10#?

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Answer 1 · 2016-01-26T09:09:47

#x=color(red)(5), color(blue)(2/3)#

Gather all terms on one side.

#3x^2-2x-15x+10=0"#

Combine like terms.

#3x^2-17x+10=0# is a quadratic equation in the form #ax^2+bx+c#, where #a=3, b=-17, c=10#.

Use the quadratic formula to solve the equation.

#x=(-b+-sqrt(b^2-4ac))/(2a)#

Substitute the values from the equation.

#x=(-(-17)+-sqrt((-17)^2-4*3*10))/(2*3)#

Simplify.

#x=(17+-sqrt(289-120))/6#

Simplify.

#x=(17+-sqrt 169)/6#

Simplify.

#x=(17+-13)/6#

Solve for #x#.

#color(red)(x=(17+13)/6)#

#color(red)(x=30/6)#

#color(red)(x=5)#

#color(blue)(x=(17-13)/6)#

#color(blue)(x=4/6)#

Reduce the fraction.

#color(blue)(x=2/3)#