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X+1/4X=6
We move all terms to the left:
X+1/4X-(6)=0
Domain of the equation: 4X!=0We multiply all the terms by the denominator
X!=0/4
X!=0
X∈R
X*4X-6*4X+1=0
Wy multiply elements
4X^2-24X+1=0
a = 4; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·4·1
Δ = 560
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{35}}{2*4}=\frac{24-4\sqrt{35}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{35}}{2*4}=\frac{24+4\sqrt{35}}{8} $
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