-1/5x-2=1/2x+7

Solution for -1/5x-2=1/2x+7 equation:

-1/5x-2=1/2x+7

We move all terms to the left:

-1/5x-2-(1/2x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

-1/5x-1/2x-7-2=0

We calculate fractions


(-2x)/10x^2+(-5x)/10x^2-7-2=0

We add all the numbers together, and all the variables

(-2x)/10x^2+(-5x)/10x^2-9=0

We multiply all the terms by the denominator


(-2x)+(-5x)-9*10x^2=0

Wy multiply elements

-90x^2+(-2x)+(-5x)=0

We get rid of parentheses

-90x^2-2x-5x=0

We add all the numbers together, and all the variables

-90x^2-7x=0

a = -90; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-90)·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*-90}=\frac{0}{-180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-90}=\frac{14}{-180}
=-7/90
$