Question

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

Answer 1

b.
`(7+√(61) )/(6) ,(7-√(61) )/(6)`

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±}{} (√(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)±(√((-7)^2-4(3)(-1)) )/(2(3))`

Evaluate The Exponent

`x=(7±√((49)-4(3)(-1)) )/(2(3))`

Multiply The Numbers

`x=(7±√(49+12) )/(2(3))`

Add The Numbers

`x=(7±√(61) )/(2(3))`

Multiply The Numbers

`x=(7±√(61) )/(6)`