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Solving a quadratic equation using the quadratic formulaWorked example

The quadratic formula can be used to solve any quadratic equation but is best saved for when an equation cannot be factorised.

Part of MathsAlgebraic skills

Worked example

Solve \(2{x^2} - 5x - 6 = 0\)

Answer

Since this quadratic cannot be factorised, use the quadratic formula, where a = 2, b = -5 and c = -6.

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

\(x = \frac{{ - ( - 5) \pm \sqrt {{{( - 5)}^2} - (4 \times 2 \times ( - 6))} }}{{2 \times 2}}\)

\(x = \frac{{5 \pm \sqrt {25 - ( - 48)} }}{4}\)

\(x = \frac{{5 \pm \sqrt {25 + 48} }}{4}\)

\(x = \frac{{5 \pm \sqrt {73} }}{4}\)

We split this into two calculations

\(x = \frac{{5 + \sqrt {73} }}{4}\)

\(x=\frac{13.544}{4}\)

\(x = 3.39\,(to\,2\,d.p.)\)

And:

\(x = \frac{{5 - \sqrt {73} }}{4}\)

\(x=\frac{-3.544}{4}\)

\(x = - 0.89\,(to\,2\,d.p.)\)

Therefore \(x = 3.39\,and\,x = - 0.89\)

(The quadratic formula will work for any quadratic equation 鈥 even if it can be factorised. However using factorisation, where possible, is usually quicker).

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