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GB-19-03-001 · Quadratic formula

Solve 5x2+4x−15=05x^{2} + 4x - 15=0. Give your answers correct to 3 significant figures.

Solving Equations: Quadratic Formula Booklet p. 13
Method
1) Identify a, b, c from ax² + bx + c = 0
2) Sub into x = (−(b) ± √((b)² − 4(a)(c))) / (2(a))
3) Evaluate with + then − to 3 s.f.
Worked Example (GB-19-03-001)
a=5,b=4,c=−15\mathbf{a = 5,\quad b = 4,\quad c = -15} \quad (Booklet p. 13: Sub into bracketed template!)
x=−()±()2−4()()2()  ⇒  x=−(4)±(4)2−4(5)(−15)2(5)=−4±31610x = \frac{-(\quad) \pm \sqrt{(\quad)^2 - 4(\quad)(\quad)}}{2(\quad)} \;\Rightarrow\; x = \frac{-(4) \pm \sqrt{(4)^2 - 4(5)(-15)}}{2(5)} = \frac{-4 \pm \sqrt{316}}{10}
With +:  x=−4+31610\text{With } + :\; x = \frac{-4 + \sqrt{316}}{10}
With −:  x=−4−31610\text{With } - :\; x = \frac{-4 - \sqrt{316}}{10}
x=1.38x=1.38 or x=−2.18x=-2.18