3/8x+6=-5/5x+5

Solution for 3/8x+6=-5/5x+5 equation:

3/8x+6=-5/5x+5

We move all terms to the left:

3/8x+6-(-5/5x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

3/8x+5/5x-5+6=0

We calculate fractions


15x/40x^2+40x/40x^2-5+6=0

We add all the numbers together, and all the variables

15x/40x^2+40x/40x^2+1=0

We multiply all the terms by the denominator


15x+40x+1*40x^2=0

We add all the numbers together, and all the variables

55x+1*40x^2=0

Wy multiply elements

40x^2+55x=0

a = 40; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·40·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*40}=\frac{-110}{80}
=-1+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*40}=\frac{0}{80}
=0
$