Question

Solve the equation by using the quadratic formula.
3 x squared minus 1 = 7 x

Answer 1

Answer:

b.  $\frac{7+\sqrt{61} }{6} ,\frac{7-\sqrt{61} }{6}$

Step-by-step explanation:

$3x^{2} -1=7x$

Quadratic equations are suppose to be written as: $ax^2+bx+c=0$

so the new quadratic equation for this problem will be: $3x^{2} -1-7x=0$

Now rearrange the terms: $3x^{2} -7x-1=0$

Then use the Quadratic Formula to Solve for the Quadratic Equation

Quadratic Formula = $x=\frac{-b±}{} \frac{\sqrt{b^2-4ac} }{2a}$

Note: Ignore the A in the quadratic formula

Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.

$3x^{2} -7x-1=0$

a = 3

b = -7

c = -1

$x=-(-7)±\frac{\sqrt{(-7)^2-4(3)(-1)} }{2(3)}$

Evaluate The Exponent

$x=\frac{7±\sqrt{(49)-4(3)(-1)} }{2(3)}$

Multiply The Numbers

$x=\frac{7±\sqrt{49+12} }{2(3)}$

Add The Numbers

$x=\frac{7±\sqrt{61} }{2(3)}$

Multiply The Numbers

$x=\frac{7±\sqrt{61} }{6}$