5/2z+6=3/4z+8

Solution for 5/2z+6=3/4z+8 equation:

5/2z+6=3/4z+8

We move all terms to the left:

5/2z+6-(3/4z+8)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z+8)!=0

z∈R


We get rid of parentheses

5/2z-3/4z-8+6=0

We calculate fractions


20z/8z^2+(-6z)/8z^2-8+6=0

We add all the numbers together, and all the variables

20z/8z^2+(-6z)/8z^2-2=0

We multiply all the terms by the denominator


20z+(-6z)-2*8z^2=0

Wy multiply elements

-16z^2+20z+(-6z)=0

We get rid of parentheses

-16z^2+20z-6z=0

We add all the numbers together, and all the variables

-16z^2+14z=0

a = -16; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-16)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-16}=\frac{-28}{-32}
=7/8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-16}=\frac{0}{-32}
=0
$