21/5x+41/3x=-98

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Solution for 21/5x+41/3x=-98 equation: 



21/5x+41/3x=-98

We move all terms to the left:

21/5x+41/3x-(-98)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R





Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

21/5x+41/3x+98=0

We calculate fractions


63x/15x^2+205x/15x^2+98=0

We multiply all the terms by the denominator


63x+205x+98*15x^2=0

We add all the numbers together, and all the variables

268x+98*15x^2=0

Wy multiply elements

1470x^2+268x=0

a = 1470; b = 268; c = 0;
Δ = b2-4ac
Δ = 2682-4·1470·0
Δ = 71824
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{71824}=268$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(268)-268}{2*1470}=\frac{-536}{2940}
=-134/735
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(268)+268}{2*1470}=\frac{0}{2940}
=0
$

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