74/5a-5/6=7/30a

Solution for 74/5a-5/6=7/30a equation:

74/5a-5/6=7/30a

We move all terms to the left:

74/5a-5/6-(7/30a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R



Domain of the equation: 30a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

74/5a-(+7/30a)-5/6=0

We get rid of parentheses

74/5a-7/30a-5/6=0

We calculate fractions


(-2250a^2)/5400a^2+79920a/5400a^2+(-1260a)/5400a^2=0

We multiply all the terms by the denominator


(-2250a^2)+79920a+(-1260a)=0

We get rid of parentheses

-2250a^2+79920a-1260a=0

We add all the numbers together, and all the variables

-2250a^2+78660a=0

a = -2250; b = 78660; c = 0;
Δ = b2-4ac
Δ = 786602-4·(-2250)·0
Δ = 6187395600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6187395600}=78660$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78660)-78660}{2*-2250}=\frac{-157320}{-4500}
=34+24/25
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78660)+78660}{2*-2250}=\frac{0}{-4500}
=0
$