(1)/(4x)=(5)/(6x)-7

Solution for (1)/(4x)=(5)/(6x)-7 equation:

(1)/(4x)=(5)/(6x)-7

We move all terms to the left:

(1)/(4x)-((5)/(6x)-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x-7)!=0

x∈R


We get rid of parentheses

1/4x-5/6x+7=0

We calculate fractions


6x/24x^2+(-20x)/24x^2+7=0

We multiply all the terms by the denominator


6x+(-20x)+7*24x^2=0

Wy multiply elements

168x^2+6x+(-20x)=0

We get rid of parentheses

168x^2+6x-20x=0

We add all the numbers together, and all the variables

168x^2-14x=0

a = 168; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·168·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*168}=\frac{28}{336}
=1/12
$