4/1a-12=4/5a+6

Solution for 4/1a-12=4/5a+6 equation:

4/1a-12=4/5a+6

We move all terms to the left:

4/1a-12-(4/5a+6)=0


Domain of the equation: 1a!=0

a∈R



Domain of the equation: 5a+6)!=0

a∈R


We get rid of parentheses

4/1a-4/5a-6-12=0

We calculate fractions


20a/5a^2+(-4a)/5a^2-6-12=0

We add all the numbers together, and all the variables

20a/5a^2+(-4a)/5a^2-18=0

We multiply all the terms by the denominator


20a+(-4a)-18*5a^2=0

Wy multiply elements

-90a^2+20a+(-4a)=0

We get rid of parentheses

-90a^2+20a-4a=0

We add all the numbers together, and all the variables

-90a^2+16a=0

a = -90; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-90)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-90}=\frac{-32}{-180}
=8/45
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-90}=\frac{0}{-180}
=0
$