2/5d-3/10=4/7d+6=14

Solution for 2/5d-3/10=4/7d+6=14 equation:

2/5d-3/10=4/7d+6=14

We move all terms to the left:

2/5d-3/10-(4/7d+6)=0


Domain of the equation: 5d!=0

d!=0/5

d!=0

d∈R



Domain of the equation: 7d+6)!=0

d∈R


We get rid of parentheses

2/5d-4/7d-6-3/10=0

We calculate fractions


(-735d^2)/350d^2+140d/350d^2+(-200d)/350d^2-6=0

We multiply all the terms by the denominator


(-735d^2)+140d+(-200d)-6*350d^2=0

Wy multiply elements

(-735d^2)-2100d^2+140d+(-200d)=0

We get rid of parentheses

-735d^2-2100d^2+140d-200d=0

We add all the numbers together, and all the variables

-2835d^2-60d=0

a = -2835; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-2835)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-2835}=\frac{0}{-5670}
=0
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-2835}=\frac{120}{-5670}
=-4/189
$