-2/3x+4x+120=170

Solution for -2/3x+4x+120=170 equation:

-2/3x+4x+120=170

We move all terms to the left:

-2/3x+4x+120-(170)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4x-2/3x-50=0

We multiply all the terms by the denominator


4x*3x-50*3x-2=0

Wy multiply elements

12x^2-150x-2=0

a = 12; b = -150; c = -2;
Δ = b2-4ac
Δ = -1502-4·12·(-2)
Δ = 22596
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:

$\sqrt{\Delta}=\sqrt{22596}=\sqrt{4*5649}=\sqrt{4}*\sqrt{5649}=2\sqrt{5649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5649}}{2*12}=\frac{150-2\sqrt{5649}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5649}}{2*12}=\frac{150+2\sqrt{5649}}{24}
$