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

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

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

We move all terms to the left:

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


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 3a-5)!=0

a∈R


We get rid of parentheses

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

We calculate fractions


9a/12a^2+(-8a)/12a^2+5+1=0

We add all the numbers together, and all the variables

9a/12a^2+(-8a)/12a^2+6=0

We multiply all the terms by the denominator


9a+(-8a)+6*12a^2=0

Wy multiply elements

72a^2+9a+(-8a)=0

We get rid of parentheses

72a^2+9a-8a=0

We add all the numbers together, and all the variables

72a^2+a=0

a = 72; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·72·0
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*72}=\frac{-2}{144}
=-1/72
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*72}=\frac{0}{144}
=0
$