/6x-20=10x-50

Solution for /6x-20=10x-50 equation:

/6x-20=10x-50

We move all terms to the left:

/6x-20-(10x-50)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

/6x-10x+50-20=0

We multiply all the terms by the denominator


-10x*6x+50*6x-20*6x+=0

We add all the numbers together, and all the variables

-10x*6x+50*6x-20*6x=0

Wy multiply elements

-60x^2+300x-120x=0

We add all the numbers together, and all the variables

-60x^2+180x=0

a = -60; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-60)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-60}=\frac{-360}{-120}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-60}=\frac{0}{-120}
=0
$