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(H)=-5H^2+45H+50
We move all terms to the left:
(H)-(-5H^2+45H+50)=0
We get rid of parentheses
5H^2-45H+H-50=0
We add all the numbers together, and all the variables
5H^2-44H-50=0
a = 5; b = -44; c = -50;
Δ = b2-4ac
Δ = -442-4·5·(-50)
Δ = 2936
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}$$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2936}=\sqrt{4*734}=\sqrt{4}*\sqrt{734}=2\sqrt{734}$$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{734}}{2*5}=\frac{44-2\sqrt{734}}{10} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{734}}{2*5}=\frac{44+2\sqrt{734}}{10} $
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