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4d(3d-2)=22d-2
We move all terms to the left:
4d(3d-2)-(22d-2)=0
We multiply parentheses
12d^2-8d-(22d-2)=0
We get rid of parentheses
12d^2-8d-22d+2=0
We add all the numbers together, and all the variables
12d^2-30d+2=0
a = 12; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·12·2
Δ = 804
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}$$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{201}}{2*12}=\frac{30-2\sqrt{201}}{24} $$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{201}}{2*12}=\frac{30+2\sqrt{201}}{24} $
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