-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^2-34x=0

a = 240; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·240·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*240}=\frac{0}{480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*240}=\frac{68}{480}
=17/120
$