Question

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

Answer 1

Answer:

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) $\sf x=\frac{-b+\sqrt{b^2-4ab} }{2b}$

2) $\sf x=\frac{-b-\sqrt{b^2-4ab} }{2b}$

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

$\sf x=\frac{8+\sqrt{(-8)^2-4\times6} }{2} ,\frac{8-\sqrt{(-8)^2-4\times6} }{2}$

Simplify,

$\sf x=\frac{8+2\sqrt{10} }{2} ,\frac{8-2\sqrt{10} }{2}$

Simplify,

$\sf x=4+\sqrt{10}, 4-\sqrt{10}$

Hope it helps!