Question

What are the solutions to 3x^2 = 8x — 6?

Answer 1

First, let's move all terms to one side,

`\sf x^2-8x+6=0`

When given this form (ax^2+bx+c=0), there will be two solutions at the end.

1)
`\sf x=(-b+√(b^2-4ab) )/(2b)`

2)
`\sf x=(-b-√(b^2-4ab) )/(2b)`

where, a=1, b=-8, c=6

`\sf x=(8+√((-8)^2-4*6) )/(2) ,(8-√((-8)^2-4*6) )/(2)`

Simplify,

`\sf x=(8+2√(10) )/(2) ,(8-2√(10) )/(2)`

Simplify,

`\sf x=4+√(10), 4-√(10)`

Hope it helps!