3/2d-1=4/5d+5

Solution for 3/2d-1=4/5d+5 equation:

3/2d-1=4/5d+5

We move all terms to the left:

3/2d-1-(4/5d+5)=0


Domain of the equation: 2d!=0

d!=0/2

d!=0

d∈R



Domain of the equation: 5d+5)!=0

d∈R


We get rid of parentheses

3/2d-4/5d-5-1=0

We calculate fractions


15d/10d^2+(-8d)/10d^2-5-1=0

We add all the numbers together, and all the variables

15d/10d^2+(-8d)/10d^2-6=0

We multiply all the terms by the denominator


15d+(-8d)-6*10d^2=0

Wy multiply elements

-60d^2+15d+(-8d)=0

We get rid of parentheses

-60d^2+15d-8d=0

We add all the numbers together, and all the variables

-60d^2+7d=0

a = -60; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-60)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$d_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-60}=\frac{-14}{-120}
=7/60
$
$d_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-60}=\frac{0}{-120}
=0
$