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 $ax^{2}+bx+c=0$.
$$-16t^{2}+90t+14=0$$
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 $t=\frac{-90±2\sqrt{2249}}{-32}$ when $±$ is plus. Add $-90$ to $2\sqrt{2249}$.
$$t=\frac{2\sqrt{2249}-90}{-32}$$
Divide $-90+2\sqrt{2249}$ by $-32$.
$$t=\frac{45-\sqrt{2249}}{16}$$
Now solve the equation $t=\frac{-90±2\sqrt{2249}}{-32}$ when $±$ is minus. Subtract $2\sqrt{2249}$ from $-90$.
$$t=\frac{-2\sqrt{2249}-90}{-32}$$
Divide $-90-2\sqrt{2249}$ by $-32$.
$$t=\frac{\sqrt{2249}+45}{16}$$
Factor the original expression using $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$. Substitute $\frac{45-\sqrt{2249}}{16}$ for $x_{1}$ and $\frac{45+\sqrt{2249}}{16}$ for $x_{2}$.
