3/8x-1/5x=7

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Solution for 3/8x-1/5x=7 equation:



3/8x-1/5x=7
We move all terms to the left:
3/8x-1/5x-(7)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We calculate fractions
15x/40x^2+(-8x)/40x^2-7=0
We multiply all the terms by the denominator
15x+(-8x)-7*40x^2=0
Wy multiply elements
-280x^2+15x+(-8x)=0
We get rid of parentheses
-280x^2+15x-8x=0
We add all the numbers together, and all the variables
-280x^2+7x=0
a = -280; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-280)·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*-280}=\frac{-14}{-560} =1/40 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-280}=\frac{0}{-560} =0 $

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