4/3x-10/4x-11=1

Solution for 4/3x-10/4x-11=1 equation:

4/3x-10/4x-11=1

We move all terms to the left:

4/3x-10/4x-11-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-10/4x-12=0

We calculate fractions


16x/12x^2+(-30x)/12x^2-12=0

We multiply all the terms by the denominator


16x+(-30x)-12*12x^2=0

Wy multiply elements

-144x^2+16x+(-30x)=0

We get rid of parentheses

-144x^2+16x-30x=0

We add all the numbers together, and all the variables

-144x^2-14x=0

a = -144; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·(-144)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*-144}=\frac{28}{-288}
=-7/72
$