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X+1/4X=15
We move all terms to the left:
X+1/4X-(15)=0
Domain of the equation: 4X!=0We multiply all the terms by the denominator
X!=0/4
X!=0
X∈R
X*4X-15*4X+1=0
Wy multiply elements
4X^2-60X+1=0
a = 4; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·4·1
Δ = 3584
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3584}=\sqrt{256*14}=\sqrt{256}*\sqrt{14}=16\sqrt{14}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-16\sqrt{14}}{2*4}=\frac{60-16\sqrt{14}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+16\sqrt{14}}{2*4}=\frac{60+16\sqrt{14}}{8} $
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