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=5+24H-16H^2
We move all terms to the left:
-(5+24H-16H^2)=0
We get rid of parentheses
16H^2-24H-5=0
a = 16; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·16·(-5)
Δ = 896
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}$$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{14}}{2*16}=\frac{24-8\sqrt{14}}{32} $$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{14}}{2*16}=\frac{24+8\sqrt{14}}{32} $
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