4/5x-1/2-7/10x=-4

Solution for 4/5x-1/2-7/10x=-4 equation:

4/5x-1/2-7/10x=-4

We move all terms to the left:

4/5x-1/2-7/10x-(-4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-7/10x+4-1/2=0

We calculate fractions


(-50x^2)/200x^2+160x/200x^2+(-140x)/200x^2+4=0

We multiply all the terms by the denominator


(-50x^2)+160x+(-140x)+4*200x^2=0

Wy multiply elements

(-50x^2)+800x^2+160x+(-140x)=0

We get rid of parentheses

-50x^2+800x^2+160x-140x=0

We add all the numbers together, and all the variables

750x^2+20x=0

a = 750; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·750·0
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*750}=\frac{-40}{1500}
=-2/75
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*750}=\frac{0}{1500}
=0
$