9(x)=2/3x-5

Solution for 9(x)=2/3x-5 equation:

9(x)=2/3x-5

We move all terms to the left:

9(x)-(2/3x-5)=0


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

x∈R


We get rid of parentheses

9x-2/3x+5=0

We multiply all the terms by the denominator


9x*3x+5*3x-2=0

Wy multiply elements

27x^2+15x-2=0

a = 27; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·27·(-2)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-21}{2*27}=\frac{-36}{54}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+21}{2*27}=\frac{6}{54}
=1/9
$