3/4x+4=1/5x+5

Solution for 3/4x+4=1/5x+5 equation:

3/4x+4=1/5x+5

We move all terms to the left:

3/4x+4-(1/5x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


15x/20x^2+(-4x)/20x^2-5+4=0

We add all the numbers together, and all the variables

15x/20x^2+(-4x)/20x^2-1=0

We multiply all the terms by the denominator


15x+(-4x)-1*20x^2=0

Wy multiply elements

-20x^2+15x+(-4x)=0

We get rid of parentheses

-20x^2+15x-4x=0

We add all the numbers together, and all the variables

-20x^2+11x=0

a = -20; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-20)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-20}=\frac{-22}{-40}
=11/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-20}=\frac{0}{-40}
=0
$