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(H)=-16H^2+48H+4
We move all terms to the left:
(H)-(-16H^2+48H+4)=0
We get rid of parentheses
16H^2-48H+H-4=0
We add all the numbers together, and all the variables
16H^2-47H-4=0
a = 16; b = -47; c = -4;
Δ = b2-4ac
Δ = -472-4·16·(-4)
Δ = 2465
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{-(-47)-\sqrt{2465}}{2*16}=\frac{47-\sqrt{2465}}{32} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2465}}{2*16}=\frac{47+\sqrt{2465}}{32} $
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