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(H)=-16H^2+160H+9
We move all terms to the left:
(H)-(-16H^2+160H+9)=0
We get rid of parentheses
16H^2-160H+H-9=0
We add all the numbers together, and all the variables
16H^2-159H-9=0
a = 16; b = -159; c = -9;
Δ = b2-4ac
Δ = -1592-4·16·(-9)
Δ = 25857
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25857}=\sqrt{1521*17}=\sqrt{1521}*\sqrt{17}=39\sqrt{17}$$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-39\sqrt{17}}{2*16}=\frac{159-39\sqrt{17}}{32} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+39\sqrt{17}}{2*16}=\frac{159+39\sqrt{17}}{32} $
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