1/4x-2=-6+15/14x

Solution for 1/4x-2=-6+15/14x equation:

1/4x-2=-6+15/14x

We move all terms to the left:

1/4x-2-(-6+15/14x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 14x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x-(15/14x-6)-2=0

We get rid of parentheses

1/4x-15/14x+6-2=0

We calculate fractions


14x/56x^2+(-60x)/56x^2+6-2=0

We add all the numbers together, and all the variables

14x/56x^2+(-60x)/56x^2+4=0

We multiply all the terms by the denominator


14x+(-60x)+4*56x^2=0

Wy multiply elements

224x^2+14x+(-60x)=0

We get rid of parentheses

224x^2+14x-60x=0

We add all the numbers together, and all the variables

224x^2-46x=0

a = 224; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·224·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*224}=\frac{0}{448}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*224}=\frac{92}{448}
=23/112
$