Solve 1.5b^2-20=0

$$1.5 b ^ { 2 } - 20 = 0$$

Solve for b

$$b = \frac{2 \sqrt{30}}{3} \approx 3.651483717$$

$$b = -\frac{2 \sqrt{30}}{3} \approx -3.651483717$$

Steps by Finding Square Root

Add 20 to both sides. Anything plus zero gives itself.

$$1.5b^{2}=20$$

Divide both sides by 1.5.

$$b^{2}=\frac{20}{1.5}$$

Expand \frac{20}{1.5} by multiplying both numerator and the denominator by 10.

$$b^{2}=\frac{200}{15}$$

Reduce the fraction \frac{200}{15} to lowest terms by extracting and canceling out 5.

$$b^{2}=\frac{40}{3}$$

Take the square root of both sides of the equation.

$$b=\frac{2\sqrt{30}}{3} b=-\frac{2\sqrt{30}}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$1.5b^{2}-20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.5 for a, 0 for b, and -20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 1.5\left(-20\right)}}{2\times 1.5}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 1.5\left(-20\right)}}{2\times 1.5}$$

Multiply -4 times 1.5.

$$b=\frac{0±\sqrt{-6\left(-20\right)}}{2\times 1.5}$$

Multiply -6 times -20.

$$b=\frac{0±\sqrt{120}}{2\times 1.5}$$

Take the square root of 120.

$$b=\frac{0±2\sqrt{30}}{2\times 1.5}$$

Multiply 2 times 1.5.

$$b=\frac{0±2\sqrt{30}}{3}$$

Now solve the equation b=\frac{0±2\sqrt{30}}{3} when ± is plus.

$$b=\frac{2\sqrt{30}}{3}$$

Now solve the equation b=\frac{0±2\sqrt{30}}{3} when ± is minus.

$$b=-\frac{2\sqrt{30}}{3}$$

The equation is now solved.

$$b=\frac{2\sqrt{30}}{3} b=-\frac{2\sqrt{30}}{3}$$