1/2x-4/5x=40

Solution for 1/2x-4/5x=40 equation:

1/2x-4/5x=40

We move all terms to the left:

1/2x-4/5x-(40)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


5x/10x^2+(-8x)/10x^2-40=0

We multiply all the terms by the denominator


5x+(-8x)-40*10x^2=0

Wy multiply elements

-400x^2+5x+(-8x)=0

We get rid of parentheses

-400x^2+5x-8x=0

We add all the numbers together, and all the variables

-400x^2-3x=0

a = -400; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-400)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-400}=\frac{0}{-800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-400}=\frac{6}{-800}
=-3/400
$