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1/5x+48+32=x
We move all terms to the left:
1/5x+48+32-(x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
-1x+1/5x+80=0
We multiply all the terms by the denominator
-1x*5x+80*5x+1=0
Wy multiply elements
-5x^2+400x+1=0
a = -5; b = 400; c = +1;
Δ = b2-4ac
Δ = 4002-4·(-5)·1
Δ = 160020
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{160020}=\sqrt{36*4445}=\sqrt{36}*\sqrt{4445}=6\sqrt{4445}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-6\sqrt{4445}}{2*-5}=\frac{-400-6\sqrt{4445}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+6\sqrt{4445}}{2*-5}=\frac{-400+6\sqrt{4445}}{-10} $
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