-3/2a+29/6+1/7a=1307/294

Solution for -3/2a+29/6+1/7a=1307/294 equation:

-3/2a+29/6+1/7a=1307/294

We move all terms to the left:

-3/2a+29/6+1/7a-(1307/294)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R



Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R


We add all the numbers together, and all the variables

-3/2a+1/7a+29/6-(+1307/294)=0

We get rid of parentheses

-3/2a+1/7a+29/6-1307/294=0

We calculate fractions


(-768516a^2)/148176a^2+835548a^2/148176a^2+(-222264a)/148176a^2+21168a/148176a^2=0

We multiply all the terms by the denominator


(-768516a^2)+835548a^2+(-222264a)+21168a=0

We add all the numbers together, and all the variables

835548a^2+(-768516a^2)+21168a+(-222264a)=0

We get rid of parentheses

835548a^2-768516a^2+21168a-222264a=0

We add all the numbers together, and all the variables

67032a^2-201096a=0

a = 67032; b = -201096; c = 0;
Δ = b2-4ac
Δ = -2010962-4·67032·0
Δ = 40439601216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40439601216}=201096$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-201096)-201096}{2*67032}=\frac{0}{134064}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-201096)+201096}{2*67032}=\frac{402192}{134064}
=3
$