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6x-4/10x+20=0
Domain of the equation: 10x!=0We multiply all the terms by the denominator
x!=0/10
x!=0
x∈R
6x*10x+20*10x-4=0
Wy multiply elements
60x^2+200x-4=0
a = 60; b = 200; c = -4;
Δ = b2-4ac
Δ = 2002-4·60·(-4)
Δ = 40960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40960}=\sqrt{4096*10}=\sqrt{4096}*\sqrt{10}=64\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-64\sqrt{10}}{2*60}=\frac{-200-64\sqrt{10}}{120} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+64\sqrt{10}}{2*60}=\frac{-200+64\sqrt{10}}{120} $
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