1*1/2*z-2=31/4*z-9

Solution for 1*1/2*z-2=31/4*z-9 equation:

1*1/2z-2=31/4z-9

We move all terms to the left:

1*1/2z-2-(31/4z-9)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R



Domain of the equation: 4z-9)!=0

z∈R


We get rid of parentheses

1*1/2z-31/4z+9-2=0

We calculate fractions


16z/8z^2+(-62z)/8z^2+9-2=0

We add all the numbers together, and all the variables

16z/8z^2+(-62z)/8z^2+7=0

We multiply all the terms by the denominator


16z+(-62z)+7*8z^2=0

Wy multiply elements

56z^2+16z+(-62z)=0

We get rid of parentheses

56z^2+16z-62z=0

We add all the numbers together, and all the variables

56z^2-46z=0

a = 56; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·56·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*56}=\frac{0}{112}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*56}=\frac{92}{112}
=23/28
$