5/4z+13/16z-5/4=5/2

Solution for 5/4z+13/16z-5/4=5/2 equation:

5/4z+13/16z-5/4=5/2

We move all terms to the left:

5/4z+13/16z-5/4-(5/2)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 16z!=0

z!=0/16

z!=0

z∈R


We add all the numbers together, and all the variables

5/4z+13/16z-5/4-(+5/2)=0

We get rid of parentheses

5/4z+13/16z-5/4-5/2=0

We calculate fractions


(-1280z^2)/2048z^2+320z/2048z^2+1664z/2048z^2+(-320z)/2048z^2=0

We multiply all the terms by the denominator


(-1280z^2)+320z+1664z+(-320z)=0

We add all the numbers together, and all the variables

(-1280z^2)+1984z+(-320z)=0

We get rid of parentheses

-1280z^2+1984z-320z=0

We add all the numbers together, and all the variables

-1280z^2+1664z=0

a = -1280; b = 1664; c = 0;
Δ = b2-4ac
Δ = 16642-4·(-1280)·0
Δ = 2768896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2768896}=1664$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1664)-1664}{2*-1280}=\frac{-3328}{-2560}
=1+3/10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1664)+1664}{2*-1280}=\frac{0}{-2560}
=0
$