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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 5a+4)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


5a/10a^2+(-6a)/10a^2-4-2=0

We add all the numbers together, and all the variables

5a/10a^2+(-6a)/10a^2-6=0

We multiply all the terms by the denominator


5a+(-6a)-6*10a^2=0

Wy multiply elements

-60a^2+5a+(-6a)=0

We get rid of parentheses

-60a^2+5a-6a=0

We add all the numbers together, and all the variables

-60a^2-1a=0

a = -60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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