Given the general quadratic equation:
[tex]ax^2+bx+c=0[/tex]
The general solution of the quadratic equation is given by the expression:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
From the problem, we have the quadratic equation:
[tex]3x{}^2+2x-225=0[/tex]
Identifying the coefficients:
[tex]\begin{gathered} a=3 \\ b=2 \\ c=-225 \end{gathered}[/tex]
Then, using the general solution formula:
[tex]\begin{gathered} x=\frac{-2\pm\sqrt{4+2700}}{6}=\frac{-2\pm52}{6} \\ \\ \Rightarrow x_1=\frac{25}{3} \\ \\ \Rightarrow x_2=-9 \end{gathered}[/tex]
And the solutions on the number line are:
