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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)!=0We get rid of parentheses
x∈R
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 $
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