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x = -b +/- sqrt(b² - 4ac)2a

April 8, 2026Mathematics

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Answer

x = \frac{-7 \pm \sqrt{229}}{6}

3 steps

To solve the quadratic equation $3x^2 + 7x - 15 = 0$ , we use the quadratic formula:

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

In this equation, we have:
$a = 3$
$b = 7$
$c = -15$

Substitute the values of $a$ , $b$ , and $c$ into the quadratic formula.
$x = \frac{-(7) \pm \sqrt{(7)^2 - 4(3)(-15)}}{2(3)}$
Simplify the terms inside the square root and the denominator.
$x = \frac{-7 \pm \sqrt{49 - (-180)}}{6}$ $x = \frac{-7 \pm \sqrt{49 + 180}}{6}$ $x = \frac{-7 \pm \sqrt{229}}{6}$
Calculate the two possible values for $x$ .
$x_1 = \frac{-7 + \sqrt{229}}{6}$ $x_2 = \frac{-7 - \sqrt{229}}{6}$
The exact solutions are:
$x_1 = \frac{-7 + \sqrt{229}}{6}$ $x_2 = \frac{-7 - \sqrt{229}}{6}$