3/5x-9=1/4x-10

Solution for 3/5x-9=1/4x-10 equation:

3/5x-9=1/4x-10

We move all terms to the left:

3/5x-9-(1/4x-10)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-10)!=0

x∈R


We get rid of parentheses

3/5x-1/4x+10-9=0

We calculate fractions


12x/20x^2+(-5x)/20x^2+10-9=0

We add all the numbers together, and all the variables

12x/20x^2+(-5x)/20x^2+1=0

We multiply all the terms by the denominator


12x+(-5x)+1*20x^2=0

Wy multiply elements

20x^2+12x+(-5x)=0

We get rid of parentheses

20x^2+12x-5x=0

We add all the numbers together, and all the variables

20x^2+7x=0

a = 20; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·20·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*20}=\frac{-14}{40}
=-7/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*20}=\frac{0}{40}
=0
$