360=2/3x+4x-170

Solution for 360=2/3x+4x-170 equation:

360=2/3x+4x-170

We move all terms to the left:

360-(2/3x+4x-170)=0


Domain of the equation: 3x+4x-170)!=0

x∈R


We add all the numbers together, and all the variables

-(4x+2/3x-170)+360=0

We get rid of parentheses

-4x-2/3x+170+360=0

We multiply all the terms by the denominator


-4x*3x+170*3x+360*3x-2=0

Wy multiply elements

-12x^2+510x+1080x-2=0

We add all the numbers together, and all the variables

-12x^2+1590x-2=0

a = -12; b = 1590; c = -2;
Δ = b2-4ac
Δ = 15902-4·(-12)·(-2)
Δ = 2528004
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:

$\sqrt{\Delta}=\sqrt{2528004}=\sqrt{4*632001}=\sqrt{4}*\sqrt{632001}=2\sqrt{632001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1590)-2\sqrt{632001}}{2*-12}=\frac{-1590-2\sqrt{632001}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1590)+2\sqrt{632001}}{2*-12}=\frac{-1590+2\sqrt{632001}}{-24}
$