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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-64x^2)/200x^2+100x/200x^2+(-150x)/200x^2+5=0

We multiply all the terms by the denominator


(-64x^2)+100x+(-150x)+5*200x^2=0

Wy multiply elements

(-64x^2)+1000x^2+100x+(-150x)=0

We get rid of parentheses

-64x^2+1000x^2+100x-150x=0

We add all the numbers together, and all the variables

936x^2-50x=0

a = 936; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·936·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*936}=\frac{0}{1872}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*936}=\frac{100}{1872}
=25/468
$