Solve 80*y+20+8*y^2

$$80 \cdot y + 20 + 8 \cdot y ^ { 2 }$$

Factor

$$8\left(y-\left(-\frac{3\sqrt{10}}{2}-5\right)\right)\left(y-\left(\frac{3\sqrt{10}}{2}-5\right)\right)$$

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.

$$8y^{2}+80y+20=0$$

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.

$$y=\frac{-80±\sqrt{80^{2}-4\times 8\times 20}}{2\times 8}$$

Square 80.

$$y=\frac{-80±\sqrt{6400-4\times 8\times 20}}{2\times 8}$$

Multiply -4 times 8.

$$y=\frac{-80±\sqrt{6400-32\times 20}}{2\times 8}$$

Multiply -32 times 20.

$$y=\frac{-80±\sqrt{6400-640}}{2\times 8}$$

Add 6400 to -640.

$$y=\frac{-80±\sqrt{5760}}{2\times 8}$$

Take the square root of 5760.

$$y=\frac{-80±24\sqrt{10}}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{-80±24\sqrt{10}}{16}$$

Now solve the equation y=\frac{-80±24\sqrt{10}}{16} when ± is plus. Add -80 to 24\sqrt{10}.

$$y=\frac{24\sqrt{10}-80}{16}$$

Divide -80+24\sqrt{10} by 16.

$$y=\frac{3\sqrt{10}}{2}-5$$

Now solve the equation y=\frac{-80±24\sqrt{10}}{16} when ± is minus. Subtract 24\sqrt{10} from -80.

$$y=\frac{-24\sqrt{10}-80}{16}$$

Divide -80-24\sqrt{10} by 16.

$$y=-\frac{3\sqrt{10}}{2}-5$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute -5+\frac{3\sqrt{10}}{2} for x_{1} and -5-\frac{3\sqrt{10}}{2} for x_{2}.

$$8y^{2}+80y+20=8\left(y-\left(\frac{3\sqrt{10}}{2}-5\right)\right)\left(y-\left(-\frac{3\sqrt{10}}{2}-5\right)\right)$$

Evaluate

$$8y^{2}+80y+20$$