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X+5/4X=54
We move all terms to the left:
X+5/4X-(54)=0
Domain of the equation: 4X!=0We multiply all the terms by the denominator
X!=0/4
X!=0
X∈R
X*4X-54*4X+5=0
Wy multiply elements
4X^2-216X+5=0
a = 4; b = -216; c = +5;
Δ = b2-4ac
Δ = -2162-4·4·5
Δ = 46576
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46576}=\sqrt{16*2911}=\sqrt{16}*\sqrt{2911}=4\sqrt{2911}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-4\sqrt{2911}}{2*4}=\frac{216-4\sqrt{2911}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+4\sqrt{2911}}{2*4}=\frac{216+4\sqrt{2911}}{8} $
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