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5x+36=1/213x+9
We move all terms to the left:
5x+36-(1/213x+9)=0
Domain of the equation: 213x+9)!=0We get rid of parentheses
x∈R
5x-1/213x-9+36=0
We multiply all the terms by the denominator
5x*213x-9*213x+36*213x-1=0
Wy multiply elements
1065x^2-1917x+7668x-1=0
We add all the numbers together, and all the variables
1065x^2+5751x-1=0
a = 1065; b = 5751; c = -1;
Δ = b2-4ac
Δ = 57512-4·1065·(-1)
Δ = 33078261
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5751)-\sqrt{33078261}}{2*1065}=\frac{-5751-\sqrt{33078261}}{2130} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5751)+\sqrt{33078261}}{2*1065}=\frac{-5751+\sqrt{33078261}}{2130} $
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