3/5x-6=-1/6x+7

Solution for 3/5x-6=-1/6x+7 equation:

3/5x-6=-1/6x+7

We move all terms to the left:

3/5x-6-(-1/6x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/5x+1/6x-7-6=0

We calculate fractions


18x/30x^2+5x/30x^2-7-6=0

We add all the numbers together, and all the variables

18x/30x^2+5x/30x^2-13=0

We multiply all the terms by the denominator


18x+5x-13*30x^2=0

We add all the numbers together, and all the variables

23x-13*30x^2=0

Wy multiply elements

-390x^2+23x=0

a = -390; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-390)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-390}=\frac{-46}{-780}
=23/390
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-390}=\frac{0}{-780}
=0
$