7/12a-7=1/4a

Solution for 7/12a-7=1/4a equation:

7/12a-7=1/4a

We move all terms to the left:

7/12a-7-(1/4a)=0


Domain of the equation: 12a!=0

a!=0/12

a!=0

a∈R



Domain of the equation: 4a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

7/12a-(+1/4a)-7=0

We get rid of parentheses

7/12a-1/4a-7=0

We calculate fractions


28a/48a^2+(-12a)/48a^2-7=0

We multiply all the terms by the denominator


28a+(-12a)-7*48a^2=0

Wy multiply elements

-336a^2+28a+(-12a)=0

We get rid of parentheses

-336a^2+28a-12a=0

We add all the numbers together, and all the variables

-336a^2+16a=0

a = -336; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-336)·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*-336}=\frac{-32}{-672}
=1/21
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-336}=\frac{0}{-672}
=0
$