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Answer:
[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]
Step-by-step explanation:
The quadratic equation is:
[tex]3x^2 - 10x + 5 = 0[/tex]
The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]
are
[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
in this case we have a = 3, b = -10, and c = 5
So, substituting for a, b and c we get
[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]
[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]
[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]
Simplifying we get
[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex] (First root/solution)
[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex] (Second root/solution)