6-5/6x=7/^-4

Solution for 6-5/6x=7/^-4 equation:

6-5/6x=7/^-4

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


()/6x^2+(-42x)/6x^2+6+4=0

We add all the numbers together, and all the variables

()/6x^2+(-42x)/6x^2+10=0

We multiply all the terms by the denominator


(-42x)+10*6x^2+()=0

We add all the numbers together, and all the variables

(-42x)+10*6x^2=0

Wy multiply elements

60x^2+(-42x)=0

We get rid of parentheses

60x^2-42x=0

a = 60; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·60·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*60}=\frac{0}{120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*60}=\frac{84}{120}
=7/10
$