4r-14=9/4r

Solution for 4r-14=9/4r equation:

4r-14=9/4r

We move all terms to the left:

4r-14-(9/4r)=0


Domain of the equation: 4r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

4r-(+9/4r)-14=0

We get rid of parentheses

4r-9/4r-14=0

We multiply all the terms by the denominator


4r*4r-14*4r-9=0

Wy multiply elements

16r^2-56r-9=0

a = 16; b = -56; c = -9;
Δ = b2-4ac
Δ = -562-4·16·(-9)
Δ = 3712
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:

$\sqrt{\Delta}=\sqrt{3712}=\sqrt{64*58}=\sqrt{64}*\sqrt{58}=8\sqrt{58}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-8\sqrt{58}}{2*16}=\frac{56-8\sqrt{58}}{32}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+8\sqrt{58}}{2*16}=\frac{56+8\sqrt{58}}{32}
$