-19/6a-5/3a=29/4

Solution for -19/6a-5/3a=29/4 equation:

-19/6a-5/3a=29/4

We move all terms to the left:

-19/6a-5/3a-(29/4)=0


Domain of the equation: 6a!=0

a!=0/6

a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We add all the numbers together, and all the variables

-19/6a-5/3a-(+29/4)=0

We get rid of parentheses

-19/6a-5/3a-29/4=0

We calculate fractions


(-1566a^2)/288a^2+(-912a)/288a^2+(-480a)/288a^2=0

We multiply all the terms by the denominator


(-1566a^2)+(-912a)+(-480a)=0

We get rid of parentheses

-1566a^2-912a-480a=0

We add all the numbers together, and all the variables

-1566a^2-1392a=0

a = -1566; b = -1392; c = 0;
Δ = b2-4ac
Δ = -13922-4·(-1566)·0
Δ = 1937664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1937664}=1392$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1392)-1392}{2*-1566}=\frac{0}{-3132}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1392)+1392}{2*-1566}=\frac{2784}{-3132}
=-8/9
$