factor 15x^2-17x-42 — step-by-step solution

Let's factor in

ℝ

15 x^{2} - 17 x - 42

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-17)}^{2} - 4 \cdot 15 \cdot (-42)

ℹ

{(-17)}^{2}

289

‖

4 \cdot 15

60

Δ = 289 + 60 \cdot 42

Δ = 289 + 2520

Δ = 2809

Since

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{17 - \sqrt{2809}}{2 \cdot 15}

ℹ

- \sqrt{2809}

-53

‖

2 \cdot 15

30

x1 = \frac{17 - 53}{30}

x1 = - \frac{36}{30}

x1 = - \frac{6}{5}

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{17 + \sqrt{2809}}{2 \cdot 15}

ℹ

\sqrt{2809}

53

‖

2 \cdot 15

30

x2 = \frac{17 + 53}{30}

x2 = \frac{70}{30}

x2 = \frac{7}{3}

▶Factors found:

15 \cdot (x + \frac{6}{5}) \cdot (x - \frac{7}{3})