x+(4/3x-5)+(4/3x)=85

Solution for x+(4/3x-5)+(4/3x)=85 equation:

x+(4/3x-5)+(4/3x)=85

We move all terms to the left:

x+(4/3x-5)+(4/3x)-(85)=0


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

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+(4/3x-5)+(+4/3x)-85=0

We get rid of parentheses

x+4/3x+4/3x-5-85=0

We multiply all the terms by the denominator


x*3x-5*3x-85*3x+4+4=0

We add all the numbers together, and all the variables

x*3x-5*3x-85*3x+8=0

Wy multiply elements

3x^2-15x-255x+8=0

We add all the numbers together, and all the variables

3x^2-270x+8=0

a = 3; b = -270; c = +8;
Δ = b2-4ac
Δ = -2702-4·3·8
Δ = 72804
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:

$\sqrt{\Delta}=\sqrt{72804}=\sqrt{4*18201}=\sqrt{4}*\sqrt{18201}=2\sqrt{18201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18201}}{2*3}=\frac{270-2\sqrt{18201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18201}}{2*3}=\frac{270+2\sqrt{18201}}{6}
$