Solve 5x^2+8x-15=

$$5 { x }^{ 2 } +8x-15=$$

Factor

$$5\left(x-\frac{-\sqrt{91}-4}{5}\right)\left(x-\frac{\sqrt{91}-4}{5}\right)$$

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.

$$5x^{2}+8x-15=0$$

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.

$$x=\frac{-8±\sqrt{8^{2}-4\times 5\left(-15\right)}}{2\times 5}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\times 5\left(-15\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{-8±\sqrt{64-20\left(-15\right)}}{2\times 5}$$

Multiply -20 times -15.

$$x=\frac{-8±\sqrt{64+300}}{2\times 5}$$

Add 64 to 300.

$$x=\frac{-8±\sqrt{364}}{2\times 5}$$

Take the square root of 364.

$$x=\frac{-8±2\sqrt{91}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{-8±2\sqrt{91}}{10}$$

Now solve the equation x=\frac{-8±2\sqrt{91}}{10} when ± is plus. Add -8 to 2\sqrt{91}.

$$x=\frac{2\sqrt{91}-8}{10}$$

Divide -8+2\sqrt{91} by 10.

$$x=\frac{\sqrt{91}-4}{5}$$

Now solve the equation x=\frac{-8±2\sqrt{91}}{10} when ± is minus. Subtract 2\sqrt{91} from -8.

$$x=\frac{-2\sqrt{91}-8}{10}$$

Divide -8-2\sqrt{91} by 10.

$$x=\frac{-\sqrt{91}-4}{5}$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{-4+\sqrt{91}}{5} for x_{1} and \frac{-4-\sqrt{91}}{5} for x_{2}.

$$5x^{2}+8x-15=5\left(x-\frac{\sqrt{91}-4}{5}\right)\left(x-\frac{-\sqrt{91}-4}{5}\right)$$

Evaluate

$$5x^{2}+8x-15$$