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2x+16=2/5x-5
We move all terms to the left:
2x+16-(2/5x-5)=0
Domain of the equation: 5x-5)!=0We get rid of parentheses
x∈R
2x-2/5x+5+16=0
We multiply all the terms by the denominator
2x*5x+5*5x+16*5x-2=0
Wy multiply elements
10x^2+25x+80x-2=0
We add all the numbers together, and all the variables
10x^2+105x-2=0
a = 10; b = 105; c = -2;
Δ = b2-4ac
Δ = 1052-4·10·(-2)
Δ = 11105
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{-(105)-\sqrt{11105}}{2*10}=\frac{-105-\sqrt{11105}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11105}}{2*10}=\frac{-105+\sqrt{11105}}{20} $
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