The quadartic equation is 3x^2+10x+8=3.
Simplify the quadratic equation to obtain the equation in standard form ax^2+bx+c=0.
[tex]\begin{gathered} 3x^2+10x+8=3 \\ 3x^2+10x+5=0 \end{gathered}[/tex]The coefficent of x^2 is a=3, coefficient of x is b=10 and constant term is c=5.
The quadartic formula for the values of x is,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]Substitute the values in the formula to obtain the value of x.
[tex]\begin{gathered} x=\frac{-10\pm\sqrt[]{(10)^2-4\cdot3\cdot5}}{2\cdot3} \\ =\frac{-10\pm\sqrt[]{100-60}}{6} \\ =\frac{-10\pm\sqrt[]{40}}{6} \\ =\frac{-10\pm2\sqrt[]{10}}{6} \\ =\frac{-5\pm\sqrt[]{10}}{3} \end{gathered}[/tex]The value of x is,
[tex]\frac{-5\pm\sqrt[]{10}}{3}[/tex]