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5x+1=1/2x+16
We move all terms to the left:
5x+1-(1/2x+16)=0
Domain of the equation: 2x+16)!=0We get rid of parentheses
x∈R
5x-1/2x-16+1=0
We multiply all the terms by the denominator
5x*2x-16*2x+1*2x-1=0
Wy multiply elements
10x^2-32x+2x-1=0
We add all the numbers together, and all the variables
10x^2-30x-1=0
a = 10; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·10·(-1)
Δ = 940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{235}}{2*10}=\frac{30-2\sqrt{235}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{235}}{2*10}=\frac{30+2\sqrt{235}}{20} $
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