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(H)=16H^2+46H+7
We move all terms to the left:
(H)-(16H^2+46H+7)=0
We get rid of parentheses
-16H^2+H-46H-7=0
We add all the numbers together, and all the variables
-16H^2-45H-7=0
a = -16; b = -45; c = -7;
Δ = b2-4ac
Δ = -452-4·(-16)·(-7)
Δ = 1577
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{-(-45)-\sqrt{1577}}{2*-16}=\frac{45-\sqrt{1577}}{-32} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1577}}{2*-16}=\frac{45+\sqrt{1577}}{-32} $
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