(12)2/3x+7x=90

Solution for (12)2/3x+7x=90 equation:

(12)2/3x+7x=90

We move all terms to the left:

(12)2/3x+7x-(90)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7x+122/3x-90=0

We multiply all the terms by the denominator


7x*3x-90*3x+122=0

Wy multiply elements

21x^2-270x+122=0

a = 21; b = -270; c = +122;
Δ = b2-4ac
Δ = -2702-4·21·122
Δ = 62652
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:

$\sqrt{\Delta}=\sqrt{62652}=\sqrt{4*15663}=\sqrt{4}*\sqrt{15663}=2\sqrt{15663}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{15663}}{2*21}=\frac{270-2\sqrt{15663}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{15663}}{2*21}=\frac{270+2\sqrt{15663}}{42}
$