1/11x-2=1/16x-12

Solution for 1/11x-2=1/16x-12 equation:

1/11x-2=1/16x-12

We move all terms to the left:

1/11x-2-(1/16x-12)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 16x-12)!=0

x∈R


We get rid of parentheses

1/11x-1/16x+12-2=0

We calculate fractions


16x/176x^2+(-11x)/176x^2+12-2=0

We add all the numbers together, and all the variables

16x/176x^2+(-11x)/176x^2+10=0

We multiply all the terms by the denominator


16x+(-11x)+10*176x^2=0

Wy multiply elements

1760x^2+16x+(-11x)=0

We get rid of parentheses

1760x^2+16x-11x=0

We add all the numbers together, and all the variables

1760x^2+5x=0

a = 1760; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·1760·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*1760}=\frac{-10}{3520}
=-1/352
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*1760}=\frac{0}{3520}
=0
$