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+22=0

We multiply all the terms by the denominator


56x+66x+22*42x^2=0

We add all the numbers together, and all the variables

122x+22*42x^2=0

Wy multiply elements

924x^2+122x=0

a = 924; b = 122; c = 0;
Δ = b2-4ac
Δ = 1222-4·924·0
Δ = 14884
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14884}=122$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(122)-122}{2*924}=\frac{-244}{1848}
=-61/462
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(122)+122}{2*924}=\frac{0}{1848}
=0
$