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x+3/4x=126
We move all terms to the left:
x+3/4x-(126)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
x*4x-126*4x+3=0
Wy multiply elements
4x^2-504x+3=0
a = 4; b = -504; c = +3;
Δ = b2-4ac
Δ = -5042-4·4·3
Δ = 253968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{253968}=\sqrt{16*15873}=\sqrt{16}*\sqrt{15873}=4\sqrt{15873}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-504)-4\sqrt{15873}}{2*4}=\frac{504-4\sqrt{15873}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-504)+4\sqrt{15873}}{2*4}=\frac{504+4\sqrt{15873}}{8} $
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