Solve 16a^2+6a-3=

$$16 { a }^{ 2 } +6a-3=$$

Factor

$$16\left(a-\frac{-\sqrt{57}-3}{16}\right)\left(a-\frac{\sqrt{57}-3}{16}\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$16a^{2}+6a-3=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$a=\frac{-6±\sqrt{6^{2}-4\times 16\left(-3\right)}}{2\times 16}$$

Square 6.

$$a=\frac{-6±\sqrt{36-4\times 16\left(-3\right)}}{2\times 16}$$

Multiply -4 times 16.

$$a=\frac{-6±\sqrt{36-64\left(-3\right)}}{2\times 16}$$

Multiply -64 times -3.

$$a=\frac{-6±\sqrt{36+192}}{2\times 16}$$

Add 36 to 192.

$$a=\frac{-6±\sqrt{228}}{2\times 16}$$

Take the square root of 228.

$$a=\frac{-6±2\sqrt{57}}{2\times 16}$$

Multiply 2 times 16.

$$a=\frac{-6±2\sqrt{57}}{32}$$

Now solve the equation a=\frac{-6±2\sqrt{57}}{32} when ± is plus. Add -6 to 2\sqrt{57}.

$$a=\frac{2\sqrt{57}-6}{32}$$

Divide -6+2\sqrt{57} by 32.

$$a=\frac{\sqrt{57}-3}{16}$$

Now solve the equation a=\frac{-6±2\sqrt{57}}{32} when ± is minus. Subtract 2\sqrt{57} from -6.

$$a=\frac{-2\sqrt{57}-6}{32}$$

Divide -6-2\sqrt{57} by 32.

$$a=\frac{-\sqrt{57}-3}{16}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-3+\sqrt{57}}{16} for x_{1} and \frac{-3-\sqrt{57}}{16} for x_{2}.

$$16a^{2}+6a-3=16\left(a-\frac{\sqrt{57}-3}{16}\right)\left(a-\frac{-\sqrt{57}-3}{16}\right)$$

Evaluate

$$16a^{2}+6a-3$$