Question

Solve using the Quadratic Formula. 3x2 - 7x - 3 = 0

Answer 1

Answer:

$\displaystyle x_1=\frac{7+ \sqrt{85}}{6}\approx 2.70\\\displaystyle x_2=\frac{7- \sqrt{85}}{6}\approx -0.37$

Step-by-step explanation:

Quadratic Formula

Given the second-degree equation:

$ax^2+bx+c=0$

The solutions of the equation can be obtained by applying the formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The equation to solve is:

$3x^2-7x-3=0$

Which means the values of the coefficients are: a=3, b=-7, c=-3. Substituting the values in the formula:

$\displaystyle x=\frac{-(-7)\pm \sqrt{(-7)^2-4(3)(-3)}}{2(3)}$

$\displaystyle x=\frac{7\pm \sqrt{49+36}}{6}$

$\displaystyle x=\frac{7\pm \sqrt{85}}{6}$

There are two real solutions for this equation:

$\displaystyle x_1=\frac{7+ \sqrt{85}}{6}$

$\displaystyle x_2=\frac{7- \sqrt{85}}{6}$

The approximate values of both roots are:

$x_1\approx 2.70$

$x_2\approx -0.37$