4r+2.25r+14=5r-3/4r+1-3

Solution for 4r+2.25r+14=5r-3/4r+1-3 equation:

4r+2.25r+14=5r-3/4r+1-3

We move all terms to the left:

4r+2.25r+14-(5r-3/4r+1-3)=0


Domain of the equation: 4r+1-3)!=0

We move all terms containing r to the left, all other terms to the right

4r-3)!=-1

r∈R


We add all the numbers together, and all the variables

4r+2.25r-(5r-3/4r-2)+14=0

We add all the numbers together, and all the variables

6.25r-(5r-3/4r-2)+14=0

We get rid of parentheses

6.25r-5r+3/4r+2+14=0

We multiply all the terms by the denominator


(6.25r)*4r-5r*4r+2*4r+14*4r+3=0

We add all the numbers together, and all the variables

(+6.25r)*4r-5r*4r+2*4r+14*4r+3=0

We multiply parentheses

24r^2-5r*4r+2*4r+14*4r+3=0

Wy multiply elements

24r^2-20r^2+8r+56r+3=0

We add all the numbers together, and all the variables

4r^2+64r+3=0

a = 4; b = 64; c = +3;
Δ = b2-4ac
Δ = 642-4·4·3
Δ = 4048
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4048}=\sqrt{16*253}=\sqrt{16}*\sqrt{253}=4\sqrt{253}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{253}}{2*4}=\frac{-64-4\sqrt{253}}{8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{253}}{2*4}=\frac{-64+4\sqrt{253}}{8}
$