1/2z+7=16-3/4z

Solution for 1/2z+7=16-3/4z equation:

1/2z+7=16-3/4z

We move all terms to the left:

1/2z+7-(16-3/4z)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z)!=0

z!=0/1

z!=0

z∈R


We add all the numbers together, and all the variables

1/2z-(-3/4z+16)+7=0

We get rid of parentheses

1/2z+3/4z-16+7=0

We calculate fractions


4z/8z^2+6z/8z^2-16+7=0

We add all the numbers together, and all the variables

4z/8z^2+6z/8z^2-9=0

We multiply all the terms by the denominator


4z+6z-9*8z^2=0

We add all the numbers together, and all the variables

10z-9*8z^2=0

Wy multiply elements

-72z^2+10z=0

a = -72; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-72)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-72}=\frac{-20}{-144}
=5/36
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-72}=\frac{0}{-144}
=0
$