2/3(x)+18-3x=-87

Solution for 2/3(x)+18-3x=-87 equation:

2/3(x)+18-3x=-87

We move all terms to the left:

2/3(x)+18-3x-(-87)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+2/3x+105=0

We multiply all the terms by the denominator


-3x*3x+105*3x+2=0

Wy multiply elements

-9x^2+315x+2=0

a = -9; b = 315; c = +2;
Δ = b2-4ac
Δ = 3152-4·(-9)·2
Δ = 99297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{99297}=\sqrt{9*11033}=\sqrt{9}*\sqrt{11033}=3\sqrt{11033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-3\sqrt{11033}}{2*-9}=\frac{-315-3\sqrt{11033}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+3\sqrt{11033}}{2*-9}=\frac{-315+3\sqrt{11033}}{-18}
$