[tex]a {y}^{2} + by + c = 0 [/tex]
[tex]3 {y}^{2} + 8y + 2 = 0 [/tex]
[tex]a = 3[/tex]
[tex]b = 8[/tex]
[tex]c = 2[/tex]
_________________________________
[tex]∆ = {b}^{2} - 4ac [/tex]
[tex]∆ = ({8})^{2} - 4 \times (3) \times (2) [/tex]
[tex]∆ = 64 - 24[/tex]
[tex]∆ = 40[/tex]
_________________________________
[tex]y = \frac{ -b ± \sqrt{∆} }{2a} \\ [/tex]
##############################
[tex]y(1) = \frac{ - 8 + \sqrt{40} }{6} \\ [/tex]
[tex]y(1) = \frac{ - 8 + \sqrt{4 \times 10} }{6} \\ [/tex]
[tex]y(1) = \frac{ - 8 + 2 \sqrt{10} }{6} \\ [/tex]
[tex]y(1) = \frac{2( - 4 + \sqrt{10}) }{2 \times 3} \\ [/tex]
[tex]y(1) = \frac{ - 4 + \sqrt{10} }{3} \\ [/tex]
+++++++++++++++++++++++++++++++++++++++
[tex]y(2) = \frac{ - 8 - \sqrt{40} }{6} \\ [/tex]
[tex]y(2) = \frac{ - 8 - \sqrt{4 \times 10} }{6} \\ [/tex]
[tex]y(2) = \frac{ - 8 - 2 \sqrt{10} }{6} \\ [/tex]
[tex]y(2) = \frac{2( - 4 - \sqrt{10}) }{2 \times 3} \\ [/tex]
[tex]y(2) = \frac{ - 4 - \sqrt{10} }{3} \\ [/tex]
##############################
_________________________________
And we're done.....♥️♥️♥️♥️♥️
