Question

Solve for x3x^2 + 2x - 5 = 0

Answer 1

Explanation

Given

$3x^2+2x-5=0$$\begin{gathered} \mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:} \\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \end{gathered}$

Therefore;

$\begin{gathered} \mathrm{For\:}\quad a=3,\:b=2,\:c=-5 \\ x_{1,\:2}=\frac{-2\pm \sqrt{2^2-4\cdot \:3\left(-5\right)}}{2\cdot \:3} \\ x_{1,\:2}=\frac{-2\pm \:8}{2\cdot \:3} \\ separate\text{ solutions} \\ x_1=\frac{-2+8}{2\cdot \:3},\:x_2=\frac{-2-8}{2\cdot \:3} \\ x_1=\frac{6}{6}x_2=\frac{-10}{6} \\ x_1=1\text{ },x_2=\frac{-5}{3} \end{gathered}$

Answer:

$x_{1}=1\text{,}x_{2}=\frac{-5}{3}$