8/6x-12=11/7x-10

Solution for 8/6x-12=11/7x-10 equation:

8/6x-12=11/7x-10

We move all terms to the left:

8/6x-12-(11/7x-10)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 7x-10)!=0

x∈R


We get rid of parentheses

8/6x-11/7x+10-12=0

We calculate fractions


56x/42x^2+(-66x)/42x^2+10-12=0

We add all the numbers together, and all the variables

56x/42x^2+(-66x)/42x^2-2=0

We multiply all the terms by the denominator


56x+(-66x)-2*42x^2=0

Wy multiply elements

-84x^2+56x+(-66x)=0

We get rid of parentheses

-84x^2+56x-66x=0

We add all the numbers together, and all the variables

-84x^2-10x=0

a = -84; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-84)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-84}=\frac{0}{-168}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-84}=\frac{20}{-168}
=-5/42
$