Solving an equation with 2 square terms

Question

Consider this equation;

$$ 3x^2 + 2dx - d^2 = 0 $$

Now I need to find the value of x.I've consider using the quadratic formula but I've got 2 squared terms. I've also tried forming the equation to get x squared on one side, but than I'm not sure what to next. Any help on this?

Thank you!

Answer 1

If the question is to solve $3x^2+2dx-d^2=0$ for $x$ you can just apply the quadratic formula, getting $$x=\frac {-2d \pm \sqrt{4d^2-4 \cdot 3 \cdot (-d^2)}}{2 \cdot 3}=\frac {-2d\pm 4d}6=\frac d3,-d$$

Answer 2

$3x^2 + 2dx - d^2=3(x+d)(x-d/3)$ so $x=-d$ or $x=d/3$