7/12x=5/6x-5

Solution for 7/12x=5/6x-5 equation:

7/12x=5/6x-5

We move all terms to the left:

7/12x-(5/6x-5)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 6x-5)!=0

x∈R


We get rid of parentheses

7/12x-5/6x+5=0

We calculate fractions


42x/72x^2+(-60x)/72x^2+5=0

We multiply all the terms by the denominator


42x+(-60x)+5*72x^2=0

Wy multiply elements

360x^2+42x+(-60x)=0

We get rid of parentheses

360x^2+42x-60x=0

We add all the numbers together, and all the variables

360x^2-18x=0

a = 360; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·360·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*360}=\frac{36}{720}
=1/20
$