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(D)=-5/3D+4
We move all terms to the left:
(D)-(-5/3D+4)=0
Domain of the equation: 3D+4)!=0We get rid of parentheses
D∈R
D+5/3D-4=0
We multiply all the terms by the denominator
D*3D-4*3D+5=0
Wy multiply elements
3D^2-12D+5=0
a = 3; b = -12; c = +5;
Δ = b2-4ac
Δ = -122-4·3·5
Δ = 84
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}$$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{21}}{2*3}=\frac{12-2\sqrt{21}}{6} $$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{21}}{2*3}=\frac{12+2\sqrt{21}}{6} $
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