3/10x-2/5=1/2x-6

Solution for 3/10x-2/5=1/2x-6 equation:

3/10x-2/5=1/2x-6

We move all terms to the left:

3/10x-2/5-(1/2x-6)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

3/10x-1/2x+6-2/5=0

We calculate fractions


(-80x^2)/500x^2+150x/500x^2+(-250x)/500x^2+6=0

We multiply all the terms by the denominator


(-80x^2)+150x+(-250x)+6*500x^2=0

Wy multiply elements

(-80x^2)+3000x^2+150x+(-250x)=0

We get rid of parentheses

-80x^2+3000x^2+150x-250x=0

We add all the numbers together, and all the variables

2920x^2-100x=0

a = 2920; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·2920·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*2920}=\frac{0}{5840}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*2920}=\frac{200}{5840}
=5/146
$