Solve {l}{3ab-}{b^2=45}

$$\left. \begin{array} { l } { 3 a b - } \\ { b ^ { 2 } = 45 } \end{array} \right.$$

Solve for b

$$b=3\sqrt{5}\approx 6.708203932$$

$$b=-3\sqrt{5}\approx -6.708203932$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$b=3\sqrt{5} b=-3\sqrt{5}$$

Steps Using the Quadratic Formula

Subtract 45 from both sides.

$$b^{2}-45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-45\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-45\right)}}{2}$$

Multiply -4 times -45.

$$b=\frac{0±\sqrt{180}}{2}$$

Take the square root of 180.

$$b=\frac{0±6\sqrt{5}}{2}$$

Now solve the equation b=\frac{0±6\sqrt{5}}{2} when ± is plus.

$$b=3\sqrt{5}$$

Now solve the equation b=\frac{0±6\sqrt{5}}{2} when ± is minus.

$$b=-3\sqrt{5}$$

The equation is now solved.

$$b=3\sqrt{5} b=-3\sqrt{5}$$