Make x the subject of the formula N = (-t) / sqrt(ax + bx)

1.

Step 1: Start with the given equation.

$y = bx$

Step 2: Divide both sides by $b$.

$x = \frac{y}{b}$

x = \frac{y{b}}

2.

Step 1: Start with the given equation.

$a = \sqrt{b - d}$

Step 2: Square both sides.

$a^{2} = b - d$

Step 3: Add $d$ to both sides.

$b = a^{2} + d$

b = a^{2 + d}

3.

Step 1: Start with the given equation.

$(p - q)(p - r) = x$

Step 2: Expand the left side.

$p^{2} - pr - pq + qr = x$

Step 3: Rearrange into standard quadratic form.

$p^{2} - (q + r)p + (qr - x) = 0$

Step 4: Apply the quadratic formula, where $A = 1$, $B = -(q + r)$, $C = qr - x$.

$p = \frac{(q + r) \pm \sqrt{(q + r)^{2} - 4(1)(qr - x)}}{2}$

p = \frac{(q + r) \pm \sqrt{(q + r)^{2 - 4(qr - x)}}{2}}

4.

Step 1: Start with the given equation.

$N = \sqrt{ax + bx}$

Step 2: Factor $x$ on the right side.

$N = \sqrt{x(a + b)}$

Step 3: Square both sides.

$N^{2} = x(a + b)$

Step 4: Divide both sides by $(a + b)$.

$x = \frac{N^{2}}{a + b}$

x = \frac{N^{2}{a + b}}