Question

8y(8+y)=78-2
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Answer 1

$8y(8 + y) = 78 - 2 \\ 64 {y}^{} + 8 {y}^{2} - 76 = 0 \\ 2{y}^{2} + 16y - 19 = 0 \\ a = 2 \\ b =16 \\ c = - 19 \\ D = {b}^{2} - 4ac = {16}^{2} - 4 \times 2 \times ( - 19) = \\ = 256 + 152 = 408 \: ( \sqrt{D} =2 \sqrt{102} ) \\ y _{1} = \frac{ - 16 - 2 \sqrt{102} }{2 \times 2} = \frac{2( - 8 - \sqrt{102} )}{2 \times 2} = \frac{ - 8 - \sqrt{102} }{2} \\ y _{2} = \frac{ - 16 + 2 \sqrt{102} }{2 \times 2} = \frac{2( - 8 + \sqrt{102} )}{2 \times 2} = \frac{ - 8 + \sqrt{102} }{2}$