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(6d+8)(3d+1)=90
We move all terms to the left:
(6d+8)(3d+1)-(90)=0
We multiply parentheses ..
(+18d^2+6d+24d+8)-90=0
We get rid of parentheses
18d^2+6d+24d+8-90=0
We add all the numbers together, and all the variables
18d^2+30d-82=0
a = 18; b = 30; c = -82;
Δ = b2-4ac
Δ = 302-4·18·(-82)
Δ = 6804
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6804}=\sqrt{324*21}=\sqrt{324}*\sqrt{21}=18\sqrt{21}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-18\sqrt{21}}{2*18}=\frac{-30-18\sqrt{21}}{36} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+18\sqrt{21}}{2*18}=\frac{-30+18\sqrt{21}}{36} $
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