Solve a=frac{-4+sqrt{4^2-(-12)}}{2(-1)}

$$a = \frac { - 4 + \sqrt { 4 ^ { 2 } - ( - 12 ) } } { 2 ( - 1 ) }$$

Solve for a

$$a=2-\sqrt{7}\approx -0.645751311$$

Steps for Solving Linear Equation

Calculate 4 to the power of 2 and get 16.

$$a=\frac{-4+\sqrt{16-\left(-12\right)}}{2\left(-1\right)}$$

The opposite of -12 is 12.

$$a=\frac{-4+\sqrt{16+12}}{2\left(-1\right)}$$

Add 16 and 12 to get 28.

$$a=\frac{-4+\sqrt{28}}{2\left(-1\right)}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$a=\frac{-4+2\sqrt{7}}{2\left(-1\right)}$$

Multiply 2 and -1 to get -2.

$$a=\frac{-4+2\sqrt{7}}{-2}$$

Divide each term of -4+2\sqrt{7} by -2 to get 2-\sqrt{7}.

$$a=2-\sqrt{7}$$

Assign a

$$a≔2-\sqrt{7}$$