2/3d+4=4/5d-2

Solution for 2/3d+4=4/5d-2 equation:

2/3d+4=4/5d-2

We move all terms to the left:

2/3d+4-(4/5d-2)=0


Domain of the equation: 3d!=0

d!=0/3

d!=0

d∈R



Domain of the equation: 5d-2)!=0

d∈R


We get rid of parentheses

2/3d-4/5d+2+4=0

We calculate fractions


10d/15d^2+(-12d)/15d^2+2+4=0

We add all the numbers together, and all the variables

10d/15d^2+(-12d)/15d^2+6=0

We multiply all the terms by the denominator


10d+(-12d)+6*15d^2=0

Wy multiply elements

90d^2+10d+(-12d)=0

We get rid of parentheses

90d^2+10d-12d=0

We add all the numbers together, and all the variables

90d^2-2d=0

a = 90; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·90·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*90}=\frac{0}{180}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*90}=\frac{4}{180}
=1/45
$