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2/5x=16-11x
We move all terms to the left:
2/5x-(16-11x)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
2/5x-(-11x+16)=0
We get rid of parentheses
2/5x+11x-16=0
We multiply all the terms by the denominator
11x*5x-16*5x+2=0
Wy multiply elements
55x^2-80x+2=0
a = 55; b = -80; c = +2;
Δ = b2-4ac
Δ = -802-4·55·2
Δ = 5960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5960}=\sqrt{4*1490}=\sqrt{4}*\sqrt{1490}=2\sqrt{1490}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-2\sqrt{1490}}{2*55}=\frac{80-2\sqrt{1490}}{110} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+2\sqrt{1490}}{2*55}=\frac{80+2\sqrt{1490}}{110} $
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