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3x+9/5x+10=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x+10*5x+9=0
Wy multiply elements
15x^2+50x+9=0
a = 15; b = 50; c = +9;
Δ = b2-4ac
Δ = 502-4·15·9
Δ = 1960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-14\sqrt{10}}{2*15}=\frac{-50-14\sqrt{10}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+14\sqrt{10}}{2*15}=\frac{-50+14\sqrt{10}}{30} $
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