/3x=2x+50

Solution for /3x=2x+50 equation:

/3x=2x+50

We move all terms to the left:

/3x-(2x+50)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

/3x-2x-50=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-6x^2-150x=0

a = -6; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·(-6)·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*-6}=\frac{300}{-12}
=-25
$