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2x+25-15/10x=3
We move all terms to the left:
2x+25-15/10x-(3)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
2x-15/10x+22=0
We multiply all the terms by the denominator
2x*10x+22*10x-15=0
Wy multiply elements
20x^2+220x-15=0
a = 20; b = 220; c = -15;
Δ = b2-4ac
Δ = 2202-4·20·(-15)
Δ = 49600
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{49600}=\sqrt{1600*31}=\sqrt{1600}*\sqrt{31}=40\sqrt{31}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-40\sqrt{31}}{2*20}=\frac{-220-40\sqrt{31}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+40\sqrt{31}}{2*20}=\frac{-220+40\sqrt{31}}{40} $
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