6-1/4x=2/5x+14

Solution for 6-1/4x=2/5x+14 equation:

6-1/4x=2/5x+14

We move all terms to the left:

6-1/4x-(2/5x+14)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+14)!=0

x∈R


We get rid of parentheses

-1/4x-2/5x-14+6=0

We calculate fractions


(-5x)/20x^2+(-8x)/20x^2-14+6=0

We add all the numbers together, and all the variables

(-5x)/20x^2+(-8x)/20x^2-8=0

We multiply all the terms by the denominator


(-5x)+(-8x)-8*20x^2=0

Wy multiply elements

-160x^2+(-5x)+(-8x)=0

We get rid of parentheses

-160x^2-5x-8x=0

We add all the numbers together, and all the variables

-160x^2-13x=0

a = -160; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-160)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-160}=\frac{0}{-320}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-160}=\frac{26}{-320}
=-13/160
$