8-1/4x=2/5x+14

Solution for 8-1/4x=2/5x+14 equation:

8-1/4x=2/5x+14

We move all terms to the left:

8-1/4x-(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+8=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-120x^2+(-5x)+(-8x)=0

We get rid of parentheses

-120x^2-5x-8x=0

We add all the numbers together, and all the variables

-120x^2-13x=0

a = -120; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-120)·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*-120}=\frac{0}{-240}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-120}=\frac{26}{-240}
=-13/120
$