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3x+15/5x+25=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x+25*5x+15=0
Wy multiply elements
15x^2+125x+15=0
a = 15; b = 125; c = +15;
Δ = b2-4ac
Δ = 1252-4·15·15
Δ = 14725
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14725}=\sqrt{25*589}=\sqrt{25}*\sqrt{589}=5\sqrt{589}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-5\sqrt{589}}{2*15}=\frac{-125-5\sqrt{589}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+5\sqrt{589}}{2*15}=\frac{-125+5\sqrt{589}}{30} $
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