3/4z+1/2z+6=5

Solution for 3/4z+1/2z+6=5 equation:

3/4z+1/2z+6=5

We move all terms to the left:

3/4z+1/2z+6-(5)=0


Domain of the equation: 4z!=0

z!=0/4

z!=0

z∈R



Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

3/4z+1/2z+1=0

We calculate fractions


6z/8z^2+4z/8z^2+1=0

We multiply all the terms by the denominator


6z+4z+1*8z^2=0

We add all the numbers together, and all the variables

10z+1*8z^2=0

Wy multiply elements

8z^2+10z=0

a = 8; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·8·0
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*8}=\frac{-20}{16}
=-1+1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*8}=\frac{0}{16}
=0
$