Solve 122y^2+11y-15=

$$122 { y }^{ 2 } +11y-15=$$

Factor

$$122\left(y-\frac{-\sqrt{7441}-11}{244}\right)\left(y-\frac{\sqrt{7441}-11}{244}\right)$$

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.

$$122y^{2}+11y-15=0$$

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.

$$y=\frac{-11±\sqrt{11^{2}-4\times 122\left(-15\right)}}{2\times 122}$$

Square 11.

$$y=\frac{-11±\sqrt{121-4\times 122\left(-15\right)}}{2\times 122}$$

Multiply -4 times 122.

$$y=\frac{-11±\sqrt{121-488\left(-15\right)}}{2\times 122}$$

Multiply -488 times -15.

$$y=\frac{-11±\sqrt{121+7320}}{2\times 122}$$

Add 121 to 7320.

$$y=\frac{-11±\sqrt{7441}}{2\times 122}$$

Multiply 2 times 122.

$$y=\frac{-11±\sqrt{7441}}{244}$$

Now solve the equation y=\frac{-11±\sqrt{7441}}{244} when ± is plus. Add -11 to \sqrt{7441}.

$$y=\frac{\sqrt{7441}-11}{244}$$

Now solve the equation y=\frac{-11±\sqrt{7441}}{244} when ± is minus. Subtract \sqrt{7441} from -11.

$$y=\frac{-\sqrt{7441}-11}{244}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-11+\sqrt{7441}}{244} for x_{1} and \frac{-11-\sqrt{7441}}{244} for x_{2}.

$$122y^{2}+11y-15=122\left(y-\frac{\sqrt{7441}-11}{244}\right)\left(y-\frac{-\sqrt{7441}-11}{244}\right)$$

Evaluate

$$122y^{2}+11y-15$$