2/3x+4/3x+5x=1400

Solution for 2/3x+4/3x+5x=1400 equation:

2/3x+4/3x+5x=1400

We move all terms to the left:

2/3x+4/3x+5x-(1400)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5x+2/3x+4/3x-1400=0

We multiply all the terms by the denominator


5x*3x-1400*3x+2+4=0

We add all the numbers together, and all the variables

5x*3x-1400*3x+6=0

Wy multiply elements

15x^2-4200x+6=0

a = 15; b = -4200; c = +6;
Δ = b2-4ac
Δ = -42002-4·15·6
Δ = 17639640
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:

$\sqrt{\Delta}=\sqrt{17639640}=\sqrt{36*489990}=\sqrt{36}*\sqrt{489990}=6\sqrt{489990}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4200)-6\sqrt{489990}}{2*15}=\frac{4200-6\sqrt{489990}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4200)+6\sqrt{489990}}{2*15}=\frac{4200+6\sqrt{489990}}{30}
$