3/5x-4/6x=-5

Solution for 3/5x-4/6x=-5 equation:

3/5x-4/6x=-5

We move all terms to the left:

3/5x-4/6x-(-5)=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 add all the numbers together, and all the variables

3/5x-4/6x+5=0

We calculate fractions


18x/30x^2+(-20x)/30x^2+5=0

We multiply all the terms by the denominator


18x+(-20x)+5*30x^2=0

Wy multiply elements

150x^2+18x+(-20x)=0

We get rid of parentheses

150x^2+18x-20x=0

We add all the numbers together, and all the variables

150x^2-2x=0

a = 150; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·150·0
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*150}=\frac{0}{300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*150}=\frac{4}{300}
=1/75
$