4/5x-10/3x-11=1

Solution for 4/5x-10/3x-11=1 equation:

4/5x-10/3x-11=1

We move all terms to the left:

4/5x-10/3x-11-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

4/5x-10/3x-12=0

We calculate fractions


12x/15x^2+(-50x)/15x^2-12=0

We multiply all the terms by the denominator


12x+(-50x)-12*15x^2=0

Wy multiply elements

-180x^2+12x+(-50x)=0

We get rid of parentheses

-180x^2+12x-50x=0

We add all the numbers together, and all the variables

-180x^2-38x=0

a = -180; b = -38; c = 0;
Δ = b2-4ac
Δ = -382-4·(-180)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-38}{2*-180}=\frac{0}{-360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+38}{2*-180}=\frac{76}{-360}
=-19/90
$