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0.5(5+h)(h)=52
We move all terms to the left:
0.5(5+h)(h)-(52)=0
We add all the numbers together, and all the variables
0.5(h+5)h-52=0
We multiply parentheses
0h^2+0h-52=0
We add all the numbers together, and all the variables
h^2+h-52=0
a = 1; b = 1; c = -52;
Δ = b2-4ac
Δ = 12-4·1·(-52)
Δ = 209
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{-(1)-\sqrt{209}}{2*1}=\frac{-1-\sqrt{209}}{2} $$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{209}}{2*1}=\frac{-1+\sqrt{209}}{2} $
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