Question

Solve 3x2 + 12x = 3.

Answer 1

`3 x^(2) + 12x = 3`

`3 x^(2) + 12x - 3 = 0`
Using the quadratic formula

`x = \frac{-b (+ or -) \sqrt{b^(2 - 4ac) } }{2a}`

`x = \frac{-12 + \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}` OR
`x = \frac{-12 - \sqrt{12^(2 - 4(3)(-3)) } }{2(3)}`

`x = (-12 + √(180) )/(6)` OR
`x = (-12 - √(180) )/(6)`
∴ x = 0.236 and x = -4.236

Answer 2

The solutions to the quadratic equation are:
`x=-2+√(5),\:x=-2-√(5)`

Explanation:

To solve the quadratic equation
`3x^2+12x=3` you must:

Subtract 3 from both sides and simplify

`3x^2+12x-3=3-3\\\\3x^2+12x-3=0`

For a quadratic equation of the form
`ax^2+bx+c=0` the solutions are

`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

`\mathrm{For\:}\quad a=3,\:b=12,\:c=-3`

`x=(-12+√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12+√(180))/(2\cdot \:3)=(-12+6√(5))/(6)=(6\left(-2+√(5)\right))/(6)=-2+√(5)`

`x=(-12-√(12^2-4\cdot \:3\left(-3\right)))/(2\cdot \:3)=(-12-√(180))/(2\cdot \:3)=(-12-6√(5))/(6)=-(6\left(2+√(5)\right))/(6)=-2-√(5)`

The solutions to the quadratic equation are:

`x=-2+√(5),\:x=-2-√(5)`