How do you solve $5 x^{2} - 7 x - 3 = 0$ $5x^2 - 7x - 3 = 0$ using the quadratic formula?

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How do you solve $5 x^{2} - 7 x - 3 = 0$ $5x^2 - 7x - 3 = 0$ using the quadratic formula?

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Answer 1 · 2018-03-31T17:35:59

$x = \frac{7 + \sqrt{109}}{10}$ $x=(7+sqrt109)/10$ or $\frac{7 - \sqrt{109}}{10}$ $(7-sqrt109)/10$

Explanation:

Quadratic formula gives the solution of $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ as $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $x=(-b+-sqrt(b^2-4ac))/(2a)$

As in $5 x^{2} - 7 x - 3 = 0$ $5x^2-7x-3=0$ , $a = 5$ $a=5$ , $b = - 7$ $b=-7$ and $c = - 3$ $c=-3$

$x = \frac{- (- 7) \pm \sqrt{{(- 7)}^{2} - 4 \cdot 5 \cdot (- 3)}}{2 \cdot 5}$ $x=(-(-7)+-sqrt((-7)^2-4*5*(-3)))/(2*5)$

= $\frac{7 \pm \sqrt{49 + 60}}{10}$ $(7+-sqrt(49+60))/10$

i.e. $x = \frac{7 + \sqrt{109}}{10}$ $x=(7+sqrt109)/10$ or $\frac{7 - \sqrt{109}}{10}$ $(7-sqrt109)/10$

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How do you solve $5 x^{2} - 7 x - 3 = 0$ $5x^2 - 7x - 3 = 0$ using the quadratic formula?

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