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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


42x/6x^2+(-5x)/6x^2+4+5=0

We add all the numbers together, and all the variables

42x/6x^2+(-5x)/6x^2+9=0

We multiply all the terms by the denominator


42x+(-5x)+9*6x^2=0

Wy multiply elements

54x^2+42x+(-5x)=0

We get rid of parentheses

54x^2+42x-5x=0

We add all the numbers together, and all the variables

54x^2+37x=0

a = 54; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·54·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*54}=\frac{-74}{108}
=-37/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*54}=\frac{0}{108}
=0
$