3/4x+1/4=7/20x-4

Solution for 3/4x+1/4=7/20x-4 equation:

3/4x+1/4=7/20x-4

We move all terms to the left:

3/4x+1/4-(7/20x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 20x-4)!=0

x∈R


We get rid of parentheses

3/4x-7/20x+4+1/4=0

We calculate fractions


60x/1280x^2+(-448x)/1280x^2+20x/1280x^2+4=0

We multiply all the terms by the denominator


60x+(-448x)+20x+4*1280x^2=0

We add all the numbers together, and all the variables

80x+(-448x)+4*1280x^2=0

Wy multiply elements

5120x^2+80x+(-448x)=0

We get rid of parentheses

5120x^2+80x-448x=0

We add all the numbers together, and all the variables

5120x^2-368x=0

a = 5120; b = -368; c = 0;
Δ = b2-4ac
Δ = -3682-4·5120·0
Δ = 135424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{135424}=368$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-368)-368}{2*5120}=\frac{0}{10240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-368)+368}{2*5120}=\frac{736}{10240}
=23/320
$