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

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Solution for 34/5x-21/2x=-10 equation:



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!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
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 = b2-4ac
Δ = -372-4·100·0
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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