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June 3, 2026Mathematics

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Answer

x = \frac{3}{2}, 1

5 steps

Identify the given equation.
The equation is $2x^2 - 5x + 3 = 0$ .
Use the quadratic formula to solve for $x$ .
The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .
In this equation, $a=2$ , $b=-5$ , and $c=3$ .
Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(2)(3)}}{2(2)}$
Simplify the expression under the square root (the discriminant).
$x = \frac{5 \pm \sqrt{25 - 24}}{4}$ $x = \frac{5 \pm \sqrt{1}}{4}$
Calculate the two possible values for $x$ .
$x_1 = \frac{5 + 1}{4} = \frac{6}{4} = \frac{3}{2}$ $x_2 = \frac{5 - 1}{4} = \frac{4}{4} = 1$
The solutions are $x = \frac{3}{2}$ and $x = 1$ .
$x = \frac{3}{2}, 1$

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