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4x+1/3x=100
We move all terms to the left:
4x+1/3x-(100)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
4x*3x-100*3x+1=0
Wy multiply elements
12x^2-300x+1=0
a = 12; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·12·1
Δ = 89952
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{89952}=\sqrt{16*5622}=\sqrt{16}*\sqrt{5622}=4\sqrt{5622}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5622}}{2*12}=\frac{300-4\sqrt{5622}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5622}}{2*12}=\frac{300+4\sqrt{5622}}{24} $
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