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1/2x+x+3x=450
We move all terms to the left:
1/2x+x+3x-(450)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
4x+1/2x-450=0
We multiply all the terms by the denominator
4x*2x-450*2x+1=0
Wy multiply elements
8x^2-900x+1=0
a = 8; b = -900; c = +1;
Δ = b2-4ac
Δ = -9002-4·8·1
Δ = 809968
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{809968}=\sqrt{16*50623}=\sqrt{16}*\sqrt{50623}=4\sqrt{50623}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-900)-4\sqrt{50623}}{2*8}=\frac{900-4\sqrt{50623}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-900)+4\sqrt{50623}}{2*8}=\frac{900+4\sqrt{50623}}{16} $
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