To find the solutions of the quadratic equation [tex]\(-7x^2 - 23x + 10 = 0\)[/tex], we need to use the quadratic formula:
[tex]\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\][/tex]
For the quadratic equation [tex]\(ax^2 + bx + c = 0\)[/tex], the coefficients are [tex]\(a = -7\)[/tex], [tex]\(b = -23\)[/tex], and [tex]\(c = 10\)[/tex].
First, we'll calculate the discriminant:
[tex]\[
\Delta = b^2 - 4ac
\][/tex]
Substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex]:
[tex]\[
\Delta = (-23)^2 - 4(-7)(10)
\][/tex]
[tex]\[
\Delta = 529 + 280
\][/tex]
[tex]\[
\Delta = 809
\][/tex]
Next, substitute the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(\Delta\)[/tex] into the quadratic formula:
[tex]\[
x = \frac{-(-23) \pm \sqrt{809}}{2(-7)}
\][/tex]
Simplify the equation:
[tex]\[
x = \frac{23 \pm \sqrt{809}}{-14}
\][/tex]
Thus, the correct answer is:
C. [tex]\(\frac{-23 \pm \sqrt{809}}{-14}\)[/tex]
