11/4a-9/8a-7/2=3/14

Solution for 11/4a-9/8a-7/2=3/14 equation:

11/4a-9/8a-7/2=3/14

We move all terms to the left:

11/4a-9/8a-7/2-(3/14)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 8a!=0

a!=0/8

a!=0

a∈R


We add all the numbers together, and all the variables

11/4a-9/8a-7/2-(+3/14)=0

We get rid of parentheses

11/4a-9/8a-7/2-3/14=0

We calculate fractions


(-25088a^2)/1792a^2+(-1536a^2)/1792a^2+4928a/1792a^2+(-2016a)/1792a^2=0

We multiply all the terms by the denominator


(-25088a^2)+(-1536a^2)+4928a+(-2016a)=0

We get rid of parentheses

-25088a^2-1536a^2+4928a-2016a=0

We add all the numbers together, and all the variables

-26624a^2+2912a=0

a = -26624; b = 2912; c = 0;
Δ = b2-4ac
Δ = 29122-4·(-26624)·0
Δ = 8479744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8479744}=2912$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2912)-2912}{2*-26624}=\frac{-5824}{-53248}
=7/64
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2912)+2912}{2*-26624}=\frac{0}{-53248}
=0
$