Solve (2a+3)(2a-3)=4

$$( 2 a + 3 ) ( 2 a - 3 ) = 4$$

Solve for a

$$a = \frac{\sqrt{13}}{2} \approx 1.802775638$$

$$a = -\frac{\sqrt{13}}{2} \approx -1.802775638$$

Steps by Finding Square Root

Consider \left(2a+3\right)\left(2a-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2a\right)^{2}-9=4$$

Expand \left(2a\right)^{2}.

$$2^{2}a^{2}-9=4$$

Calculate 2 to the power of 2 and get 4.

$$4a^{2}-9=4$$

Add 9 to both sides.

$$4a^{2}=4+9$$

Add 4 and 9 to get 13.

$$4a^{2}=13$$

Divide both sides by 4.

$$a^{2}=\frac{13}{4}$$

Take the square root of both sides of the equation.

$$a=\frac{\sqrt{13}}{2} a=-\frac{\sqrt{13}}{2}$$

Steps Using the Quadratic Formula

Consider \left(2a+3\right)\left(2a-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$\left(2a\right)^{2}-9=4$$

Expand \left(2a\right)^{2}.

$$2^{2}a^{2}-9=4$$

Calculate 2 to the power of 2 and get 4.

$$4a^{2}-9=4$$

Subtract 4 from both sides.

$$4a^{2}-9-4=0$$

Subtract 4 from -9 to get -13.

$$4a^{2}-13=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -13 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\times 4\left(-13\right)}}{2\times 4}$$

Square 0.

$$a=\frac{0±\sqrt{-4\times 4\left(-13\right)}}{2\times 4}$$

Multiply -4 times 4.

$$a=\frac{0±\sqrt{-16\left(-13\right)}}{2\times 4}$$

Multiply -16 times -13.

$$a=\frac{0±\sqrt{208}}{2\times 4}$$

Take the square root of 208.

$$a=\frac{0±4\sqrt{13}}{2\times 4}$$

Multiply 2 times 4.

$$a=\frac{0±4\sqrt{13}}{8}$$

Now solve the equation a=\frac{0±4\sqrt{13}}{8} when ± is plus.

$$a=\frac{\sqrt{13}}{2}$$

Now solve the equation a=\frac{0±4\sqrt{13}}{8} when ± is minus.

$$a=-\frac{\sqrt{13}}{2}$$

The equation is now solved.

$$a=\frac{\sqrt{13}}{2} a=-\frac{\sqrt{13}}{2}$$