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1/5x+14=x-107
We move all terms to the left:
1/5x+14-(x-107)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
1/5x-x+107+14=0
We multiply all the terms by the denominator
-x*5x+107*5x+14*5x+1=0
Wy multiply elements
-5x^2+535x+70x+1=0
We add all the numbers together, and all the variables
-5x^2+605x+1=0
a = -5; b = 605; c = +1;
Δ = b2-4ac
Δ = 6052-4·(-5)·1
Δ = 366045
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{-(605)-\sqrt{366045}}{2*-5}=\frac{-605-\sqrt{366045}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(605)+\sqrt{366045}}{2*-5}=\frac{-605+\sqrt{366045}}{-10} $
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