-1/2r-1/2+9/4r=-4

Solution for -1/2r-1/2+9/4r=-4 equation:

-1/2r-1/2+9/4r=-4

We move all terms to the left:

-1/2r-1/2+9/4r-(-4)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R


We add all the numbers together, and all the variables

-1/2r+9/4r+4-1/2=0

We calculate fractions


(-4r)/32r^2+72r/32r^2+(-4r)/32r^2+4=0

We multiply all the terms by the denominator


(-4r)+72r+(-4r)+4*32r^2=0

We add all the numbers together, and all the variables

72r+(-4r)+(-4r)+4*32r^2=0

Wy multiply elements

128r^2+72r+(-4r)+(-4r)=0

We get rid of parentheses

128r^2+72r-4r-4r=0

We add all the numbers together, and all the variables

128r^2+64r=0

a = 128; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·128·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*128}=\frac{-128}{256}
=-1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*128}=\frac{0}{256}
=0
$