R(x)=8/9x-17;R(x)=15

Solution for R(x)=8/9x-17;R(x)=15 equation:

(R)=8/9R-17(R)=15

We move all terms to the left:

(R)-(8/9R-17(R))=0


Domain of the equation: 9R-17R)!=0

R∈R


We add all the numbers together, and all the variables

R-(-17R+8/9R)=0

We get rid of parentheses

R+17R-8/9R=0

We multiply all the terms by the denominator


R*9R+17R*9R-8=0

Wy multiply elements

9R^2+153R^2-8=0

We add all the numbers together, and all the variables

162R^2-8=0

a = 162; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·162·(-8)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72}{2*162}=\frac{-72}{324}
=-2/9
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72}{2*162}=\frac{72}{324}
=2/9
$