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.

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

How do you solve 3x^2 – 2x = 15x – 103x^2 – 2x = 15x – 10?