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5d^2+15d+5=-6
We move all terms to the left:
5d^2+15d+5-(-6)=0
We add all the numbers together, and all the variables
5d^2+15d+11=0
a = 5; b = 15; c = +11;
Δ = b2-4ac
Δ = 152-4·5·11
Δ = 5
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{5}}{2*5}=\frac{-15-\sqrt{5}}{10} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{5}}{2*5}=\frac{-15+\sqrt{5}}{10} $
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