Solve 9b / 8 * b + 0 = 20 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$9\ b:8b-00=20$$

Solve for b

$b = \frac{4 \sqrt{10}}{3} \approx 4.216370214$
$b = -\frac{4 \sqrt{10}}{3} \approx -4.216370214$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply both sides of the equation by $8$.

$$9bb-0=160$$

Multiply $b$ and $b$ to get $b^{2}$.

$$9b^{2}-0=160$$

Add $0$ to both sides.

$$9b^{2}=160+0$$

Add $160$ and $0$ to get $160$.

$$9b^{2}=160$$

Divide both sides by $9$.

$$b^{2}=\frac{160}{9}$$

Take the square root of both sides of the equation.

$$b=\frac{4\sqrt{10}}{3}$$ $$b=-\frac{4\sqrt{10}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by $8$.

$$9bb-0=160$$

Multiply $b$ and $b$ to get $b^{2}$.

$$9b^{2}-0=160$$

Subtract $160$ from both sides.

$$9b^{2}-0-160=0$$

Reorder the terms.

$$9b^{2}-160=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $9$ for $a$, $0$ for $b$, and $-160$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$b=\frac{0±\sqrt{0^{2}-4\times 9\left(-160\right)}}{2\times 9}$$

Square $0$.

$$b=\frac{0±\sqrt{-4\times 9\left(-160\right)}}{2\times 9}$$

Multiply $-4$ times $9$.

$$b=\frac{0±\sqrt{-36\left(-160\right)}}{2\times 9}$$

Multiply $-36$ times $-160$.

$$b=\frac{0±\sqrt{5760}}{2\times 9}$$

Take the square root of $5760$.

$$b=\frac{0±24\sqrt{10}}{2\times 9}$$

Multiply $2$ times $9$.

$$b=\frac{0±24\sqrt{10}}{18}$$

Now solve the equation $b=\frac{0±24\sqrt{10}}{18}$ when $±$ is plus.

$$b=\frac{4\sqrt{10}}{3}$$

Now solve the equation $b=\frac{0±24\sqrt{10}}{18}$ when $±$ is minus.

$$b=-\frac{4\sqrt{10}}{3}$$

The equation is now solved.

$$b=\frac{4\sqrt{10}}{3}$$ $$b=-\frac{4\sqrt{10}}{3}$$