-4+4/5x-5/6x=-43/10

Solution for -4+4/5x-5/6x=-43/10 equation:

-4+4/5x-5/6x=-43/10

We move all terms to the left:

-4+4/5x-5/6x-(-43/10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

4/5x-5/6x-4+43/10=0

We calculate fractions


7740x^2/300x^2+240x/300x^2+(-250x)/300x^2-4=0

We multiply all the terms by the denominator


7740x^2+240x+(-250x)-4*300x^2=0

Wy multiply elements

7740x^2-1200x^2+240x+(-250x)=0

We get rid of parentheses

7740x^2-1200x^2+240x-250x=0

We add all the numbers together, and all the variables

6540x^2-10x=0

a = 6540; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·6540·0
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*6540}=\frac{0}{13080}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*6540}=\frac{20}{13080}
=1/654
$