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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

84x-5*320x^2=0

Wy multiply elements

-1600x^2+84x=0

a = -1600; b = 84; c = 0;
Δ = b2-4ac
Δ = 842-4·(-1600)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-84}{2*-1600}=\frac{-168}{-3200}
=21/400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+84}{2*-1600}=\frac{0}{-3200}
=0
$