3x+9/10x-40=0

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Solution for 3x+9/10x-40=0 equation: 



3x+9/10x-40=0



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



We multiply all the terms by the denominator


3x*10x-40*10x+9=0

Wy multiply elements

30x^2-400x+9=0

a = 30; b = -400; c = +9;
Δ = b2-4ac
Δ = -4002-4·30·9
Δ = 158920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:


$\sqrt{\Delta}=\sqrt{158920}=\sqrt{4*39730}=\sqrt{4}*\sqrt{39730}=2\sqrt{39730}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2\sqrt{39730}}{2*30}=\frac{400-2\sqrt{39730}}{60}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2\sqrt{39730}}{2*30}=\frac{400+2\sqrt{39730}}{60}
$

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