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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


64x/320x^2+(-15x)/320x^2+5x/320x^2-5=0

We multiply all the terms by the denominator


64x+(-15x)+5x-5*320x^2=0

We add all the numbers together, and all the variables

69x+(-15x)-5*320x^2=0

Wy multiply elements

-1600x^2+69x+(-15x)=0

We get rid of parentheses

-1600x^2+69x-15x=0

We add all the numbers together, and all the variables

-1600x^2+54x=0

a = -1600; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-1600)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-1600}=\frac{-108}{-3200}
=27/800
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-1600}=\frac{0}{-3200}
=0
$