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(H)=-10H^2+25H+5
We move all terms to the left:
(H)-(-10H^2+25H+5)=0
We get rid of parentheses
10H^2-25H+H-5=0
We add all the numbers together, and all the variables
10H^2-24H-5=0
a = 10; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·10·(-5)
Δ = 776
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}$$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{194}}{2*10}=\frac{24-2\sqrt{194}}{20} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{194}}{2*10}=\frac{24+2\sqrt{194}}{20} $
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