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1/5x+4=x-36
We move all terms to the left:
1/5x+4-(x-36)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
1/5x-x+36+4=0
We multiply all the terms by the denominator
-x*5x+36*5x+4*5x+1=0
Wy multiply elements
-5x^2+180x+20x+1=0
We add all the numbers together, and all the variables
-5x^2+200x+1=0
a = -5; b = 200; c = +1;
Δ = b2-4ac
Δ = 2002-4·(-5)·1
Δ = 40020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40020}=\sqrt{4*10005}=\sqrt{4}*\sqrt{10005}=2\sqrt{10005}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-2\sqrt{10005}}{2*-5}=\frac{-200-2\sqrt{10005}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+2\sqrt{10005}}{2*-5}=\frac{-200+2\sqrt{10005}}{-10} $
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