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135/x=4x
We move all terms to the left:
135/x-(4x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-4x+135/x=0
We multiply all the terms by the denominator
-4x*x+135=0
Wy multiply elements
-4x^2+135=0
a = -4; b = 0; c = +135;
Δ = b2-4ac
Δ = 02-4·(-4)·135
Δ = 2160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*-4}=\frac{0-12\sqrt{15}}{-8} =-\frac{12\sqrt{15}}{-8} =-\frac{3\sqrt{15}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*-4}=\frac{0+12\sqrt{15}}{-8} =\frac{12\sqrt{15}}{-8} =\frac{3\sqrt{15}}{-2} $
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