2/3x+x=70

Solution for 2/3x+x=70 equation:

2/3x+x=70

We move all terms to the left:

2/3x+x-(70)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

x+2/3x-70=0

We multiply all the terms by the denominator


x*3x-70*3x+2=0

Wy multiply elements

3x^2-210x+2=0

a = 3; b = -210; c = +2;
Δ = b2-4ac
Δ = -2102-4·3·2
Δ = 44076
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:

$\sqrt{\Delta}=\sqrt{44076}=\sqrt{4*11019}=\sqrt{4}*\sqrt{11019}=2\sqrt{11019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-2\sqrt{11019}}{2*3}=\frac{210-2\sqrt{11019}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+2\sqrt{11019}}{2*3}=\frac{210+2\sqrt{11019}}{6}
$