1/2r+2(3/4-1)=1/4r+

Solution for 1/2r+2(3/4-1)=1/4r+ equation:

1/2r+2(3/4-1)=1/4r+

We move all terms to the left:

1/2r+2(3/4-1)-(1/4r+)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r+)!=0

r∈R


We add all the numbers together, and all the variables

1/2r-(+1/4r)+2(3/4-1)=0

We multiply parentheses

1/2r-(+1/4r)-2+3/4*2=0

We get rid of parentheses

1/2r-1/4r-2+3/4*2=0

We calculate fractions


96r^2/256r^2+128r/256r^2+(-64r)/256r^2-2=0

We multiply all the terms by the denominator


96r^2+128r+(-64r)-2*256r^2=0

Wy multiply elements

96r^2-512r^2+128r+(-64r)=0

We get rid of parentheses

96r^2-512r^2+128r-64r=0

We add all the numbers together, and all the variables

-416r^2+64r=0

a = -416; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-416)·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*-416}=\frac{-128}{-832}
=2/13
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-416}=\frac{0}{-832}
=0
$