2/5x-1/2x=3/4+1

Solution for 2/5x-1/2x=3/4+1 equation:

2/5x-1/2x=3/4+1

We move all terms to the left:

2/5x-1/2x-(3/4+1)=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 get rid of parentheses

2/5x-1/2x-1-3/4=0

We calculate fractions


(-60x^2)/160x^2+64x/160x^2+(-80x)/160x^2-1=0

We multiply all the terms by the denominator


(-60x^2)+64x+(-80x)-1*160x^2=0

Wy multiply elements

(-60x^2)-160x^2+64x+(-80x)=0

We get rid of parentheses

-60x^2-160x^2+64x-80x=0

We add all the numbers together, and all the variables

-220x^2-16x=0

a = -220; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-220)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-220}=\frac{0}{-440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-220}=\frac{32}{-440}
=-4/55
$