Solve 3t^2-59t+272

$$3 { t }^{ 2 } -59t+272$$

Factor

$$3\left(t-\frac{59-\sqrt{217}}{6}\right)\left(t-\frac{\sqrt{217}+59}{6}\right)$$

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.

$$3t^{2}-59t+272=0$$

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.

$$t=\frac{-\left(-59\right)±\sqrt{\left(-59\right)^{2}-4\times 3\times 272}}{2\times 3}$$

Square -59.

$$t=\frac{-\left(-59\right)±\sqrt{3481-4\times 3\times 272}}{2\times 3}$$

Multiply -4 times 3.

$$t=\frac{-\left(-59\right)±\sqrt{3481-12\times 272}}{2\times 3}$$

Multiply -12 times 272.

$$t=\frac{-\left(-59\right)±\sqrt{3481-3264}}{2\times 3}$$

Add 3481 to -3264.

$$t=\frac{-\left(-59\right)±\sqrt{217}}{2\times 3}$$

The opposite of -59 is 59.

$$t=\frac{59±\sqrt{217}}{2\times 3}$$

Multiply 2 times 3.

$$t=\frac{59±\sqrt{217}}{6}$$

Now solve the equation t=\frac{59±\sqrt{217}}{6} when ± is plus. Add 59 to \sqrt{217}.

$$t=\frac{\sqrt{217}+59}{6}$$

Now solve the equation t=\frac{59±\sqrt{217}}{6} when ± is minus. Subtract \sqrt{217} from 59.

$$t=\frac{59-\sqrt{217}}{6}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{59+\sqrt{217}}{6} for x_{1} and \frac{59-\sqrt{217}}{6} for x_{2}.

$$3t^{2}-59t+272=3\left(t-\frac{\sqrt{217}+59}{6}\right)\left(t-\frac{59-\sqrt{217}}{6}\right)$$

Evaluate

$$3t^{2}-59t+272$$