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(H)=-12H^2+480H+30
We move all terms to the left:
(H)-(-12H^2+480H+30)=0
We get rid of parentheses
12H^2-480H+H-30=0
We add all the numbers together, and all the variables
12H^2-479H-30=0
a = 12; b = -479; c = -30;
Δ = b2-4ac
Δ = -4792-4·12·(-30)
Δ = 230881
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{-(-479)-\sqrt{230881}}{2*12}=\frac{479-\sqrt{230881}}{24} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-479)+\sqrt{230881}}{2*12}=\frac{479+\sqrt{230881}}{24} $
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