3/4r+16=4/5r-14

Solution for 3/4r+16=4/5r-14 equation:

3/4r+16=4/5r-14

We move all terms to the left:

3/4r+16-(4/5r-14)=0


Domain of the equation: 4r!=0

r!=0/4

r!=0

r∈R



Domain of the equation: 5r-14)!=0

r∈R


We get rid of parentheses

3/4r-4/5r+14+16=0

We calculate fractions


15r/20r^2+(-16r)/20r^2+14+16=0

We add all the numbers together, and all the variables

15r/20r^2+(-16r)/20r^2+30=0

We multiply all the terms by the denominator


15r+(-16r)+30*20r^2=0

Wy multiply elements

600r^2+15r+(-16r)=0

We get rid of parentheses

600r^2+15r-16r=0

We add all the numbers together, and all the variables

600r^2-1r=0

a = 600; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·600·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*600}=\frac{0}{1200}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*600}=\frac{2}{1200}
=1/600
$