Identify coefficients: Identify the coefficients of the quadratic equation 2x² + 5x − 7 = 0. Here, a = 2, b = 5, and c = -7.Use quadratic formula: Use the quadratic formula to find the solutions for x. The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a).Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: b² - 4ac. Discriminant = (5)² - 4(2)(-7) = 25 + 56 = 81.Two real solutions: Since the discriminant is positive, there will be two real solutions.Calculate solutions: Calculate the two solutions using the quadratic formula. First solution: x = [-5 + √81] / (2 * 2) = [-5 + 9] / 4 = 4 / 4 = 1. Second solution: x = [-5 - √81] / (2 * 2) = [-5 - 9] / 4 = -14 / 4 = -3.5.

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$2x^2 + 5x - 7 = 0$ .

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2x^2 + 5x - 7 = 0

Identify coefficients: Identify the coefficients of the quadratic equation $2x^2 + 5x - 7 = 0$ . Here, $a = 2$ , $b = 5$ , and $c = -7$ .
Use quadratic formula: Use the quadratic formula to find the solutions for $x$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
Calculate discriminant: Calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . Discriminant = $(5)^2 - 4(2)(-7) = 25 + 56 = 81$ .
Two real solutions: Since the discriminant is positive, there will be two real solutions.
Calculate solutions: Calculate the two solutions using the quadratic formula. $\newline$ First solution: $x = \frac{{-5 + \sqrt{81}}}{{2 \times 2}} = \frac{{-5 + 9}}{4} = \frac{4}{4} = 1$ . $\newline$ Second solution: $x = \frac{{-5 - \sqrt{81}}}{{2 \times 2}} = \frac{{-5 - 9}}{4} = \frac{-14}{4} = -3.5$ .