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

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

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

We move all terms to the left:

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


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



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

a∈R


We get rid of parentheses

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

We calculate fractions


4a/8a^2+(-6a)/8a^2+5+6=0

We add all the numbers together, and all the variables

4a/8a^2+(-6a)/8a^2+11=0

We multiply all the terms by the denominator


4a+(-6a)+11*8a^2=0

Wy multiply elements

88a^2+4a+(-6a)=0

We get rid of parentheses

88a^2+4a-6a=0

We add all the numbers together, and all the variables

88a^2-2a=0

a = 88; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·88·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*88}=\frac{0}{176}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*88}=\frac{4}{176}
=1/44
$