Final answer:
To solve the quadratic equation 5x^2 = 3x – 7, rearrange to the standard form ax^2 + bx + c = 0, and use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a) to find the roots.
Step-by-step explanation:
To solve the quadratic equation 5x^2 = 3x – 7, we first need to rearrange it to the standard form of a quadratic equation, which is ax^2 + bx + c = 0. By subtracting 3x and adding 7 to both sides of the equation, we get 5x^2 - 3x + 7 = 0. The solution or roots for this equation can be calculated using the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a). In this formula, a, b, and c are coefficients from the equation ax^2 + bx + c = 0, where a equals 5, b equals -3, and c equals 7.