r=4/3*r-5

Solution for r=4/3*r-5 equation:

r=4/3r-5

We move all terms to the left:

r-(4/3r-5)=0


Domain of the equation: 3r-5)!=0

r∈R


We get rid of parentheses

r-4/3r+5=0

We multiply all the terms by the denominator


r*3r+5*3r-4=0

Wy multiply elements

3r^2+15r-4=0

a = 3; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·3·(-4)
Δ = 273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{273}}{2*3}=\frac{-15-\sqrt{273}}{6}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{273}}{2*3}=\frac{-15+\sqrt{273}}{6}
$