x+2/3.x=135

Solution for x+2/3.x=135 equation:

x+2/3.x=135

We move all terms to the left:

x+2/3.x-(135)=0


Domain of the equation: 3.x!=0

x!=0/3.

x!=0

x∈R


We multiply all the terms by the denominator


x*3.x-135*3.x+2=0

Wy multiply elements

3x^2-405x+2=0

a = 3; b = -405; c = +2;
Δ = b2-4ac
Δ = -4052-4·3·2
Δ = 164001
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{-(-405)-\sqrt{164001}}{2*3}=\frac{405-\sqrt{164001}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-405)+\sqrt{164001}}{2*3}=\frac{405+\sqrt{164001}}{6}
$