18r-24=171/4r+3

Solution for 18r-24=171/4r+3 equation:

18r-24=171/4r+3

We move all terms to the left:

18r-24-(171/4r+3)=0


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

r∈R


We get rid of parentheses

18r-171/4r-3-24=0

We multiply all the terms by the denominator


18r*4r-3*4r-24*4r-171=0

Wy multiply elements

72r^2-12r-96r-171=0

We add all the numbers together, and all the variables

72r^2-108r-171=0

a = 72; b = -108; c = -171;
Δ = b2-4ac
Δ = -1082-4·72·(-171)
Δ = 60912
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:

$\sqrt{\Delta}=\sqrt{60912}=\sqrt{1296*47}=\sqrt{1296}*\sqrt{47}=36\sqrt{47}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-36\sqrt{47}}{2*72}=\frac{108-36\sqrt{47}}{144}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+36\sqrt{47}}{2*72}=\frac{108+36\sqrt{47}}{144}
$