-5/4a-1-5/2a=21/16

Solution for -5/4a-1-5/2a=21/16 equation:

-5/4a-1-5/2a=21/16

We move all terms to the left:

-5/4a-1-5/2a-(21/16)=0


Domain of the equation: 4a!=0

a!=0/4

a!=0

a∈R



Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-5/4a-5/2a-1-(+21/16)=0

We get rid of parentheses

-5/4a-5/2a-1-21/16=0

We calculate fractions


(-336a^2)/128a^2+(-160a)/128a^2+(-320a)/128a^2-1=0

We multiply all the terms by the denominator


(-336a^2)+(-160a)+(-320a)-1*128a^2=0

Wy multiply elements

(-336a^2)-128a^2+(-160a)+(-320a)=0

We get rid of parentheses

-336a^2-128a^2-160a-320a=0

We add all the numbers together, and all the variables

-464a^2-480a=0

a = -464; b = -480; c = 0;
Δ = b2-4ac
Δ = -4802-4·(-464)·0
Δ = 230400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{230400}=480$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-480}{2*-464}=\frac{0}{-928}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+480}{2*-464}=\frac{960}{-928}
=-1+1/29
$