4/5x-3=4/10x+7

Solution for 4/5x-3=4/10x+7 equation:

4/5x-3=4/10x+7

We move all terms to the left:

4/5x-3-(4/10x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x+7)!=0

x∈R


We get rid of parentheses

4/5x-4/10x-7-3=0

We calculate fractions


40x/50x^2+(-20x)/50x^2-7-3=0

We add all the numbers together, and all the variables

40x/50x^2+(-20x)/50x^2-10=0

We multiply all the terms by the denominator


40x+(-20x)-10*50x^2=0

Wy multiply elements

-500x^2+40x+(-20x)=0

We get rid of parentheses

-500x^2+40x-20x=0

We add all the numbers together, and all the variables

-500x^2+20x=0

a = -500; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-500)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-500}=\frac{-40}{-1000}
=1/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-500}=\frac{0}{-1000}
=0
$