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1/2X+2X=150
We move all terms to the left:
1/2X+2X-(150)=0
Domain of the equation: 2X!=0We add all the numbers together, and all the variables
X!=0/2
X!=0
X∈R
2X+1/2X-150=0
We multiply all the terms by the denominator
2X*2X-150*2X+1=0
Wy multiply elements
4X^2-300X+1=0
a = 4; b = -300; c = +1;
Δ = b2-4ac
Δ = -3002-4·4·1
Δ = 89984
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{89984}=\sqrt{64*1406}=\sqrt{64}*\sqrt{1406}=8\sqrt{1406}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-8\sqrt{1406}}{2*4}=\frac{300-8\sqrt{1406}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+8\sqrt{1406}}{2*4}=\frac{300+8\sqrt{1406}}{8} $
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