To solve the quadratic equation 3x² + 13x + 36 = 0, we will use the quadratic formula: x = (−b ± √(b² − 4ac))/(2a); Here, a=3, b=13, and c=36. Step 1: Calculate the discriminant, Δ = b² − 4ac. Δ = (13)² − 4(3)(36); Δ = 169 − 12(36); Δ = 169 − 432; Δ = −263 Step 2: Substitute the values into the quadratic formula. Since the discriminant Δ is negative, there are no real solutions. The solutions will be complex numbers. x = (−13 ± √(−263))/(2(3)); x = (−13 ± i√(263))/(6) Step 3: Write out the two complex solutions. x₁ = (−13 + i√(263))/(6); x₂ = (−13 − i√(263))/(6) The solutions are: x = (−13 ± i√(263))/(6)

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3x2 + 13x + 36 = 0

August 26, 2026Mathematics

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Answer

x = \frac{-13 \pm i\sqrt{263}}{6}

Step-by-step solution

3 steps

To solve the quadratic equation $3x^2 + 13x + 36 = 0$ , we will use the quadratic formula:

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Here, $a=3$ , $b=13$ , and $c=36$ .

Calculate the discriminant, $\Delta = b^2 - 4ac$ .
$\Delta = (13)^2 - 4(3)(36)$ $\Delta = 169 - 12(36)$ $\Delta = 169 - 432$ $\Delta = -263$
Substitute the values into the quadratic formula.
Since the discriminant $\Delta$ is negative, there are no real solutions. The solutions will be complex numbers.
$x = \frac{-13 \pm \sqrt{-263}}{2(3)}$ $x = \frac{-13 \pm i\sqrt{263}}{6}$
Write out the two complex solutions.
$x_1 = \frac{-13 + i\sqrt{263}}{6}$ $x_2 = \frac{-13 - i\sqrt{263}}{6}$

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3x2 + 13x + 36 = 0

Answer

Step-by-step solution

Calculate the discriminant, Δ=b2−4ac\Delta = b^2 - 4acΔ=b2−4ac.

Substitute the values into the quadratic formula.

Write out the two complex solutions.

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More Mathematics Questions

Calculate the discriminant, $\Delta = b^2 - 4ac$ .