31/2z+6=21/4z+5

Solution for 31/2z+6=21/4z+5 equation:

31/2z+6=21/4z+5

We move all terms to the left:

31/2z+6-(21/4z+5)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z+5)!=0

z∈R


We get rid of parentheses

31/2z-21/4z-5+6=0

We calculate fractions


124z/8z^2+(-42z)/8z^2-5+6=0

We add all the numbers together, and all the variables

124z/8z^2+(-42z)/8z^2+1=0

We multiply all the terms by the denominator


124z+(-42z)+1*8z^2=0

Wy multiply elements

8z^2+124z+(-42z)=0

We get rid of parentheses

8z^2+124z-42z=0

We add all the numbers together, and all the variables

8z^2+82z=0

a = 8; b = 82; c = 0;
Δ = b2-4ac
Δ = 822-4·8·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(82)-82}{2*8}=\frac{-164}{16}
=-10+1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(82)+82}{2*8}=\frac{0}{16}
=0
$