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2x+1/4x=135
We move all terms to the left:
2x+1/4x-(135)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
2x*4x-135*4x+1=0
Wy multiply elements
8x^2-540x+1=0
a = 8; b = -540; c = +1;
Δ = b2-4ac
Δ = -5402-4·8·1
Δ = 291568
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{291568}=\sqrt{16*18223}=\sqrt{16}*\sqrt{18223}=4\sqrt{18223}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-540)-4\sqrt{18223}}{2*8}=\frac{540-4\sqrt{18223}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-540)+4\sqrt{18223}}{2*8}=\frac{540+4\sqrt{18223}}{16} $
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