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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-20x^2)/100x^2+60x/100x^2+(-50x)/100x^2-1=0

We multiply all the terms by the denominator


(-20x^2)+60x+(-50x)-1*100x^2=0

Wy multiply elements

(-20x^2)-100x^2+60x+(-50x)=0

We get rid of parentheses

-20x^2-100x^2+60x-50x=0

We add all the numbers together, and all the variables

-120x^2+10x=0

a = -120; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-120)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-120}=\frac{-20}{-240}
=1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-120}=\frac{0}{-240}
=0
$