19/24+1/6a=1/4a

Solution for 19/24+1/6a=1/4a equation:

19/24+1/6a=1/4a

We move all terms to the left:

19/24+1/6a-(1/4a)=0


Domain of the equation: 6a!=0

a!=0/6

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

1/6a-(+1/4a)+19/24=0

We get rid of parentheses

1/6a-1/4a+19/24=0

We calculate fractions


1824a^2/1152a^2+192a/1152a^2+(-288a)/1152a^2=0

We multiply all the terms by the denominator


1824a^2+192a+(-288a)=0

We get rid of parentheses

1824a^2+192a-288a=0

We add all the numbers together, and all the variables

1824a^2-96a=0

a = 1824; b = -96; c = 0;
Δ = b2-4ac
Δ = -962-4·1824·0
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-96}{2*1824}=\frac{0}{3648}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+96}{2*1824}=\frac{192}{3648}
=1/19
$