Question

How do you solve `4x^2-6=-12x`?

Answer 1

`x=(-3+-sqrt(15))/2`

Explanation:

`4x^2-6=12x`

`rarr 4x^2+12x-6=0`

`rarr 2x^2+6x-3=0`

applying the quadratic formula:
`color(white)("XXX")x=(-6+-sqrt(6^2-4 * 2 * (-3)))/(2 * 2)`

`color(white)("XXX")=(-6+-sqrt(36+24))/4`

`color(white)("XXX")=(-cancel(6)^3+-cancel(2)sqrt(15))/(cancel(4)_2)`

You could use a calculator if you needed this in an approximate decimal form:
`color(white)("XXX")(-3+-sqrt(15))/2~~0.43691673 or -3.436491673`