3b^2+5b-16=-4 — step-by-step solution

⚠Ⓘ 3b is read as the product 3*b: for a power, write 3^b‖5b is read as the product 5*b: for a power, write 5^b

1) Let's solve in

ℝ

3 b^{2} + 5 b - 16 = -4

3 b^{2}

+ 5 b

- 16

+ 4 = 0

3 b^{2} + 5 b - 12 = 0

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = 5^{2} - 4 \cdot 3 \cdot (-12)

ℹ

5^{2}

25

‖

4 \cdot 3

12

Δ = 25 + 12 \cdot 12

Δ = 25 + 144

Δ = 169

Δ > 0

, the equation has two solutions:

For the first solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

b1 = \frac{- 5 - \sqrt{169}}{2 \cdot 3}

ℹ

- \sqrt{169}

-13

‖

2 \cdot 3

6

b1 = \frac{- 5 - 13}{6}

b1 = - \frac{18}{6}

b1 = -3

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

b2 = \frac{- 5 + \sqrt{169}}{2 \cdot 3}

ℹ

\sqrt{169}

13

‖

2 \cdot 3

6

b2 = \frac{- 5 + 13}{6}

b2 = \frac{8}{6}

b2 = \frac{4}{3}

Solution found:

b = -3

Solution obtained:

b = \frac{4}{3}

▶Solution:

b = {-3, \frac{4}{3}}

2) The numeric value of:

b = {-3, \frac{4}{3}}

is:

▷

b = {-3, \approx 1.3333}