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10d^2-55d+75=0
a = 10; b = -55; c = +75;
Δ = b2-4ac
Δ = -552-4·10·75
Δ = 25
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5}{2*10}=\frac{50}{20} =2+1/2 $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5}{2*10}=\frac{60}{20} =3 $
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