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8y(2y+4)=102

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Solution for 8y(2y+4)=102 equation:



8y(2y+4)=102
We move all terms to the left:
8y(2y+4)-(102)=0
We multiply parentheses
16y^2+32y-102=0
a = 16; b = 32; c = -102;
Δ = b2-4ac
Δ = 322-4·16·(-102)
Δ = 7552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
y_{1}=\frac{-b-\sqrt{\Delta}}{2a}
y_{2}=\frac{-b+\sqrt{\Delta}}{2a}

The end solution:
\sqrt{\Delta}=\sqrt{7552}=\sqrt{64*118}=\sqrt{64}*\sqrt{118}=8\sqrt{118}
y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{118}}{2*16}=\frac{-32-8\sqrt{118}}{32}
y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{118}}{2*16}=\frac{-32+8\sqrt{118}}{32}

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