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10d(d+4)=40
We move all terms to the left:
10d(d+4)-(40)=0
We multiply parentheses
10d^2+40d-40=0
a = 10; b = 40; c = -40;
Δ = b2-4ac
Δ = 402-4·10·(-40)
Δ = 3200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{2}}{2*10}=\frac{-40-40\sqrt{2}}{20} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{2}}{2*10}=\frac{-40+40\sqrt{2}}{20} $
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