-1/4a-4=7/9a-3

Solution for -1/4a-4=7/9a-3 equation:

-1/4a-4=7/9a-3

We move all terms to the left:

-1/4a-4-(7/9a-3)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 9a-3)!=0

a∈R


We get rid of parentheses

-1/4a-7/9a+3-4=0

We calculate fractions


(-9a)/36a^2+(-28a)/36a^2+3-4=0

We add all the numbers together, and all the variables

(-9a)/36a^2+(-28a)/36a^2-1=0

We multiply all the terms by the denominator


(-9a)+(-28a)-1*36a^2=0

Wy multiply elements

-36a^2+(-9a)+(-28a)=0

We get rid of parentheses

-36a^2-9a-28a=0

We add all the numbers together, and all the variables

-36a^2-37a=0

a = -36; b = -37; c = 0;
Δ = b2-4ac
Δ = -372-4·(-36)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*-36}=\frac{0}{-72}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*-36}=\frac{74}{-72}
=-1+1/36
$