-9a^2-49a+516=0 — step-by-step solution

1) Let's solve in

ℝ

- 9 a^{2} - 49 a + 516 = 0

Given the quadratic form

a x^{2} + b x + c

, you can calculate the discriminant:

Δ = b^{2} - 4 a c

Δ = {(-49)}^{2} - 4 \cdot (-9) \cdot 516

ℹ

{(-49)}^{2}

2401

‖

-4 \cdot (-9)

36

Δ = 2401 + 36 \cdot 516

Δ = 2401 + 18576

Δ = 20977

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

a1 = \frac{49 - \sqrt{20977}}{2 \cdot (-9)}

a1 = \frac{49 - \sqrt{20977}}{-18}

a1 = - \frac{49 - \sqrt{20977}}{18}

a1 = \frac{- 49 + \sqrt{20977}}{18}

For the second solution, we obtain:

\frac{- b + \sqrt{Δ}}{2 a}

a2 = \frac{49 + \sqrt{20977}}{2 \cdot (-9)}

a2 = \frac{49 + \sqrt{20977}}{-18}

a2 = - \frac{49 + \sqrt{20977}}{18}

Solution found:

a = - \frac{\sqrt{20977} + 49}{18}

Solution obtained:

a = \frac{\sqrt{20977} - 49}{18}

▶Solution:

a = {- \frac{\sqrt{20977} + 49}{18}, \frac{\sqrt{20977} - 49}{18}}

2) The numeric value of:

a = {- \frac{\sqrt{20977} + 49}{18}, \frac{\sqrt{20977} - 49}{18}}

is:

a = {- \frac{\approx 144.8344 + 49}{18}, \frac{\approx 144.8344 - 49}{18}}

a = {- \frac{\approx 193.8344}{18}, \frac{\approx 95.8344}{18}}

▷

a = {\approx -10.7686, \approx 5.3241}