3/4*2a-6+1/2=2/5*3a+20

Solution for 3/4*2a-6+1/2=2/5*3a+20 equation:

3/4*2a-6+1/2=2/5*3a+20

We move all terms to the left:

3/4*2a-6+1/2-(2/5*3a+20)=0


Domain of the equation: 4*2a!=0

a!=0/1

a!=0

a∈R



Domain of the equation: 5*3a+20)!=0

a∈R


We get rid of parentheses

3/4*2a-2/5*3a-20-6+1/2=0

We calculate fractions


240a^2/1200a^2+270a/1200a^2+(-64a)/1200a^2-20-6=0

We add all the numbers together, and all the variables

240a^2/1200a^2+270a/1200a^2+(-64a)/1200a^2-26=0

We multiply all the terms by the denominator


240a^2+270a+(-64a)-26*1200a^2=0

Wy multiply elements

240a^2-31200a^2+270a+(-64a)=0

We get rid of parentheses

240a^2-31200a^2+270a-64a=0

We add all the numbers together, and all the variables

-30960a^2+206a=0

a = -30960; b = 206; c = 0;
Δ = b2-4ac
Δ = 2062-4·(-30960)·0
Δ = 42436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42436}=206$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-206}{2*-30960}=\frac{-412}{-61920}
=103/15480
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+206}{2*-30960}=\frac{0}{-61920}
=0
$