3/4a-11/8a-3/4=5/2

Solution for 3/4a-11/8a-3/4=5/2 equation:

3/4a-11/8a-3/4=5/2

We move all terms to the left:

3/4a-11/8a-3/4-(5/2)=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

3/4a-11/8a-3/4-(+5/2)=0

We get rid of parentheses

3/4a-11/8a-3/4-5/2=0

We calculate fractions


(-5120a^2)/1024a^2+96a/1024a^2+(-1408a)/1024a^2+(-96a)/1024a^2=0

We multiply all the terms by the denominator


(-5120a^2)+96a+(-1408a)+(-96a)=0

We get rid of parentheses

-5120a^2+96a-1408a-96a=0

We add all the numbers together, and all the variables

-5120a^2-1408a=0

a = -5120; b = -1408; c = 0;
Δ = b2-4ac
Δ = -14082-4·(-5120)·0
Δ = 1982464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1982464}=1408$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1408)-1408}{2*-5120}=\frac{0}{-10240}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1408)+1408}{2*-5120}=\frac{2816}{-10240}
=-11/40
$