In order to solve a quadratic equation, the first step is identifying the parameters a, b and c of the standard form:
[tex]\begin{gathered} ax^2+bx+c=0\\ \\ 2x^2+5x-12=0\\ \\ a=2,\text{ }b=5,\text{ }c=-12 \end{gathered}[/tex]Now, the next step is using the quadratic formula to find the values of x:
[tex]\begin{gathered} x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-5\pm\sqrt{5^2-4\cdot2\cdot(-12)}}{2\cdot2}\\ \\ x=\frac{-5\pm11}{4}\\ \\ x_1=\frac{-5+11}{4}=\frac{6}{4}=1.5\\ \\ x_2=\frac{-5-11}{4}=\frac{-16}{4}=-4 \end{gathered}[/tex]Therefore the solutions are x = 1.5 and x = -4.
