solve 2x^2+3x-2=0 — step-by-step solution

1) Let's solve in

ℝ

2 x^{2} + 3 x - 2 = 0

Given the quadratic form

a x^{2} + b x + c

, let's compute the discriminant:

Δ = b^{2} - 4 a c

Δ = 3^{2} - 4 \cdot 2 \cdot -2

Δ = 9 + 8 \cdot 2

Δ = 9 + 16

Δ = 25

Since

Δ > 0

, the equation has two solutions:

For the 1st solution, we obtain:

\frac{- b - \sqrt{Δ}}{2 a}

x1 = \frac{- 3 - \sqrt{25}}{2 \cdot 2}

x1 = - \frac{3 + 5}{4}

x1 = - \frac{8}{4}

x1 = -2

Solution second:

\frac{- b + \sqrt{Δ}}{2 a}

x2 = \frac{- 3 + \sqrt{25}}{2 \cdot 2}

x2 = \frac{- 3 + 5}{4}

x2 = \frac{2}{4}

x2 = \frac{1}{2}

Solution obtained:

x = -2

Solution found:

x = \frac{1}{2}

2) The approximate value of:

x = {-2, \frac{1}{2}}

is:

x = {-2, 0.5}

▷Result: $x = {-2, \frac{1}{2}}$

▷▷Numeric value:

x = {-2, 0.5}