Solve 4b^2-9b^2+5=0

$$4 b ^ { 2 } - 9 b ^ { 2 } + 5 = 0$$

Solve for b

$$b=1$$

$$b=-1$$

Steps by Finding Square Root

Combine 4b^{2} and -9b^{2} to get -5b^{2}.

$$-5b^{2}+5=0$$

Subtract 5 from both sides. Anything subtracted from zero gives its negation.

$$-5b^{2}=-5$$

Divide both sides by -5.

$$b^{2}=\frac{-5}{-5}$$

Divide -5 by -5 to get 1.

$$b^{2}=1$$

Take the square root of both sides of the equation.

$$b=1 b=-1$$

Steps Using the Quadratic Formula

Combine 4b^{2} and -9b^{2} to get -5b^{2}.

$$-5b^{2}+5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 5}}{2\left(-5\right)}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-5\right)\times 5}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$b=\frac{0±\sqrt{20\times 5}}{2\left(-5\right)}$$

Multiply 20 times 5.

$$b=\frac{0±\sqrt{100}}{2\left(-5\right)}$$

Take the square root of 100.

$$b=\frac{0±10}{2\left(-5\right)}$$

Multiply 2 times -5.

$$b=\frac{0±10}{-10}$$

Now solve the equation b=\frac{0±10}{-10} when ± is plus. Divide 10 by -10.

$$b=-1$$

Now solve the equation b=\frac{0±10}{-10} when ± is minus. Divide -10 by -10.

$$b=1$$

The equation is now solved.

$$b=-1 b=1$$