6/5x-1/2x=-21

Solution for 6/5x-1/2x=-21 equation:

6/5x-1/2x=-21

We move all terms to the left:

6/5x-1/2x-(-21)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6/5x-1/2x+21=0

We calculate fractions


12x/10x^2+(-5x)/10x^2+21=0

We multiply all the terms by the denominator


12x+(-5x)+21*10x^2=0

Wy multiply elements

210x^2+12x+(-5x)=0

We get rid of parentheses

210x^2+12x-5x=0

We add all the numbers together, and all the variables

210x^2+7x=0

a = 210; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·210·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*210}=\frac{-14}{420}
=-1/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*210}=\frac{0}{420}
=0
$