R(x)=8/9x-17

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

(R)=8/9R-17

We move all terms to the left:

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


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

R∈R


We get rid of parentheses

R-8/9R+17=0

We multiply all the terms by the denominator


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

Wy multiply elements

9R^2+153R-8=0

a = 9; b = 153; c = -8;
Δ = b2-4ac
Δ = 1532-4·9·(-8)
Δ = 23697
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:

$\sqrt{\Delta}=\sqrt{23697}=\sqrt{9*2633}=\sqrt{9}*\sqrt{2633}=3\sqrt{2633}$
$R_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(153)-3\sqrt{2633}}{2*9}=\frac{-153-3\sqrt{2633}}{18}
$
$R_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(153)+3\sqrt{2633}}{2*9}=\frac{-153+3\sqrt{2633}}{18}
$