Solve x=frac{6+sqrt{-6^2-4*2*1}}{2*2}

$$x = \frac{ 6+ \sqrt{ { -6 }^{ 2 } -4 \cdot 2 \cdot 1 } }{ 2 \cdot 2 }$$

Solve for x

$$x = \frac{\sqrt{7} + 3}{2} \approx 2.822875656$$

Steps for Solving Linear Equation

Calculate -6 to the power of 2 and get 36.

$$x=\frac{6+\sqrt{36-4\times 2\times 1}}{2\times 2}$$

Multiply 4 and 2 to get 8.

$$x=\frac{6+\sqrt{36-8\times 1}}{2\times 2}$$

Multiply 8 and 1 to get 8.

$$x=\frac{6+\sqrt{36-8}}{2\times 2}$$

Subtract 8 from 36 to get 28.

$$x=\frac{6+\sqrt{28}}{2\times 2}$$

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}.

$$x=\frac{6+2\sqrt{7}}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$x=\frac{6+2\sqrt{7}}{4}$$

Divide each term of 6+2\sqrt{7} by 4 to get \frac{3}{2}+\frac{1}{2}\sqrt{7}.

$$x=\frac{3}{2}+\frac{1}{2}\sqrt{7}$$

Assign x

$$x≔\frac{\sqrt{7}+3}{2}$$