3/5x-6=-2/4x-5

Solution for 3/5x-6=-2/4x-5 equation:

3/5x-6=-2/4x-5

We move all terms to the left:

3/5x-6-(-2/4x-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

3/5x+2/4x+5-6=0

We calculate fractions


12x/20x^2+10x/20x^2+5-6=0

We add all the numbers together, and all the variables

12x/20x^2+10x/20x^2-1=0

We multiply all the terms by the denominator


12x+10x-1*20x^2=0

We add all the numbers together, and all the variables

22x-1*20x^2=0

Wy multiply elements

-20x^2+22x=0

a = -20; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-20)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-20}=\frac{-44}{-40}
=1+1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-20}=\frac{0}{-40}
=0
$