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3x-2/5x+6=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x+6*5x-2=0
Wy multiply elements
15x^2+30x-2=0
a = 15; b = 30; c = -2;
Δ = b2-4ac
Δ = 302-4·15·(-2)
Δ = 1020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{255}}{2*15}=\frac{-30-2\sqrt{255}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{255}}{2*15}=\frac{-30+2\sqrt{255}}{30} $
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