5/2r-7=3/4r+14

Solution for 5/2r-7=3/4r+14 equation:

5/2r-7=3/4r+14

We move all terms to the left:

5/2r-7-(3/4r+14)=0


Domain of the equation: 2r!=0

r!=0/2

r!=0

r∈R



Domain of the equation: 4r+14)!=0

r∈R


We get rid of parentheses

5/2r-3/4r-14-7=0

We calculate fractions


20r/8r^2+(-6r)/8r^2-14-7=0

We add all the numbers together, and all the variables

20r/8r^2+(-6r)/8r^2-21=0

We multiply all the terms by the denominator


20r+(-6r)-21*8r^2=0

Wy multiply elements

-168r^2+20r+(-6r)=0

We get rid of parentheses

-168r^2+20r-6r=0

We add all the numbers together, and all the variables

-168r^2+14r=0

a = -168; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-168)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-168}=\frac{-28}{-336}
=1/12
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-168}=\frac{0}{-336}
=0
$