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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


8x/20x^2+15x/20x^2+4+5=0

We add all the numbers together, and all the variables

8x/20x^2+15x/20x^2+9=0

We multiply all the terms by the denominator


8x+15x+9*20x^2=0

We add all the numbers together, and all the variables

23x+9*20x^2=0

Wy multiply elements

180x^2+23x=0

a = 180; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·180·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*180}=\frac{-46}{360}
=-23/180
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*180}=\frac{0}{360}
=0
$