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4x+9/5x=261
We move all terms to the left:
4x+9/5x-(261)=0
Domain of the equation: 5x!=0We multiply all the terms by the denominator
x!=0/5
x!=0
x∈R
4x*5x-261*5x+9=0
Wy multiply elements
20x^2-1305x+9=0
a = 20; b = -1305; c = +9;
Δ = b2-4ac
Δ = -13052-4·20·9
Δ = 1702305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1702305}=\sqrt{9*189145}=\sqrt{9}*\sqrt{189145}=3\sqrt{189145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1305)-3\sqrt{189145}}{2*20}=\frac{1305-3\sqrt{189145}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1305)+3\sqrt{189145}}{2*20}=\frac{1305+3\sqrt{189145}}{40} $
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