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(H)=-16H^2+130H+12
We move all terms to the left:
(H)-(-16H^2+130H+12)=0
We get rid of parentheses
16H^2-130H+H-12=0
We add all the numbers together, and all the variables
16H^2-129H-12=0
a = 16; b = -129; c = -12;
Δ = b2-4ac
Δ = -1292-4·16·(-12)
Δ = 17409
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}$$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-\sqrt{17409}}{2*16}=\frac{129-\sqrt{17409}}{32} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+\sqrt{17409}}{2*16}=\frac{129+\sqrt{17409}}{32} $
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