X+2/3x=20

Solution for X+2/3x=20 equation:

X+2/3X=20

We move all terms to the left:

X+2/3X-(20)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We multiply all the terms by the denominator


X*3X-20*3X+2=0

Wy multiply elements

3X^2-60X+2=0

a = 3; b = -60; c = +2;
Δ = b2-4ac
Δ = -602-4·3·2
Δ = 3576
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:

$\sqrt{\Delta}=\sqrt{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{894}}{2*3}=\frac{60-2\sqrt{894}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{894}}{2*3}=\frac{60+2\sqrt{894}}{6}
$