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 $ax^{2}+bx+c=0$.
$$4x^{2}-28x+30=0$$
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.
Now solve the equation $x=\frac{28±4\sqrt{19}}{8}$ when $±$ is plus. Add $28$ to $4\sqrt{19}$.
$$x=\frac{4\sqrt{19}+28}{8}$$
Divide $28+4\sqrt{19}$ by $8$.
$$x=\frac{\sqrt{19}+7}{2}$$
Now solve the equation $x=\frac{28±4\sqrt{19}}{8}$ when $±$ is minus. Subtract $4\sqrt{19}$ from $28$.
$$x=\frac{28-4\sqrt{19}}{8}$$
Divide $28-4\sqrt{19}$ by $8$.
$$x=\frac{7-\sqrt{19}}{2}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{7+\sqrt{19}}{2}$ for $x_{1}$ and $\frac{7-\sqrt{19}}{2}$ for $x_{2}$.
