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

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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 $

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