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34/5x-21/2x=-10

We move all terms to the left:

34/5x-21/2x-(-10)=0

Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R

Domain of the equation: 2x!=0We add all the numbers together, and all the variables

x!=0/2

x!=0

x∈R

34/5x-21/2x+10=0

We calculate fractions

68x/10x^2+(-105x)/10x^2+10=0

We multiply all the terms by the denominator

68x+(-105x)+10*10x^2=0

Wy multiply elements

100x^2+68x+(-105x)=0

We get rid of parentheses

100x^2+68x-105x=0

We add all the numbers together, and all the variables

100x^2-37x=0

a = 100; b = -37; c = 0;

Δ = b^{2}-4ac

Δ = -37^{2}-4·100·0

Δ = 1369

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{1369}=37$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-37}{2*100}=\frac{0}{200} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+37}{2*100}=\frac{74}{200} =37/100 $

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