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6d(4d-5)=4d+12
We move all terms to the left:
6d(4d-5)-(4d+12)=0
We multiply parentheses
24d^2-30d-(4d+12)=0
We get rid of parentheses
24d^2-30d-4d-12=0
We add all the numbers together, and all the variables
24d^2-34d-12=0
a = 24; b = -34; c = -12;
Δ = b2-4ac
Δ = -342-4·24·(-12)
Δ = 2308
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2308}=\sqrt{4*577}=\sqrt{4}*\sqrt{577}=2\sqrt{577}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{577}}{2*24}=\frac{34-2\sqrt{577}}{48} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{577}}{2*24}=\frac{34+2\sqrt{577}}{48} $
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