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2/5x+10=x+5
We move all terms to the left:
2/5x+10-(x+5)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
2/5x-x-5+10=0
We multiply all the terms by the denominator
-x*5x-5*5x+10*5x+2=0
Wy multiply elements
-5x^2-25x+50x+2=0
We add all the numbers together, and all the variables
-5x^2+25x+2=0
a = -5; b = 25; c = +2;
Δ = b2-4ac
Δ = 252-4·(-5)·2
Δ = 665
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{-(25)-\sqrt{665}}{2*-5}=\frac{-25-\sqrt{665}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{665}}{2*-5}=\frac{-25+\sqrt{665}}{-10} $
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