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4d(5+d)=68.96
We move all terms to the left:
4d(5+d)-(68.96)=0
We add all the numbers together, and all the variables
4d(d+5)-(68.96)=0
We add all the numbers together, and all the variables
4d(d+5)-68.96=0
We multiply parentheses
4d^2+20d-68.96=0
a = 4; b = 20; c = -68.96;
Δ = b2-4ac
Δ = 202-4·4·(-68.96)
Δ = 1503.36
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{-(20)-\sqrt{1503.36}}{2*4}=\frac{-20-\sqrt{1503.36}}{8} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+\sqrt{1503.36}}{2*4}=\frac{-20+\sqrt{1503.36}}{8} $
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