3/4x-4/6x=-10

Solution for 3/4x-4/6x=-10 equation:

3/4x-4/6x=-10

We move all terms to the left:

3/4x-4/6x-(-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-4/6x+10=0

We calculate fractions


18x/24x^2+(-16x)/24x^2+10=0

We multiply all the terms by the denominator


18x+(-16x)+10*24x^2=0

Wy multiply elements

240x^2+18x+(-16x)=0

We get rid of parentheses

240x^2+18x-16x=0

We add all the numbers together, and all the variables

240x^2+2x=0

a = 240; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·240·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*240}=\frac{-4}{480}
=-1/120
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*240}=\frac{0}{480}
=0
$