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3x-2/5x=212
We move all terms to the left:
3x-2/5x-(212)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
3x*5x-212*5x-2=0
Wy multiply elements
15x^2-1060x-2=0
a = 15; b = -1060; c = -2;
Δ = b2-4ac
Δ = -10602-4·15·(-2)
Δ = 1123720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1123720}=\sqrt{4*280930}=\sqrt{4}*\sqrt{280930}=2\sqrt{280930}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1060)-2\sqrt{280930}}{2*15}=\frac{1060-2\sqrt{280930}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1060)+2\sqrt{280930}}{2*15}=\frac{1060+2\sqrt{280930}}{30} $
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