x+(2/3x-15)=18

Solution for x+(2/3x-15)=18 equation:

x+(2/3x-15)=18

We move all terms to the left:

x+(2/3x-15)-(18)=0


Domain of the equation: 3x-15)!=0

x∈R


We get rid of parentheses

x+2/3x-15-18=0

We multiply all the terms by the denominator


x*3x-15*3x-18*3x+2=0

Wy multiply elements

3x^2-45x-54x+2=0

We add all the numbers together, and all the variables

3x^2-99x+2=0

a = 3; b = -99; c = +2;
Δ = b2-4ac
Δ = -992-4·3·2
Δ = 9777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-\sqrt{9777}}{2*3}=\frac{99-\sqrt{9777}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9777}}{2*3}=\frac{99+\sqrt{9777}}{6}
$