4/3x-2x=90

Solution for 4/3x-2x=90 equation:

4/3x-2x=90

We move all terms to the left:

4/3x-2x-(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

-2x+4/3x-90=0

We multiply all the terms by the denominator


-2x*3x-90*3x+4=0

Wy multiply elements

-6x^2-270x+4=0

a = -6; b = -270; c = +4;
Δ = b2-4ac
Δ = -2702-4·(-6)·4
Δ = 72996
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:

$\sqrt{\Delta}=\sqrt{72996}=\sqrt{4*18249}=\sqrt{4}*\sqrt{18249}=2\sqrt{18249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18249}}{2*-6}=\frac{270-2\sqrt{18249}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18249}}{2*-6}=\frac{270+2\sqrt{18249}}{-12}
$