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-12x+x+x+1/2x=360
We move all terms to the left:
-12x+x+x+1/2x-(360)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-10x+1/2x-360=0
We multiply all the terms by the denominator
-10x*2x-360*2x+1=0
Wy multiply elements
-20x^2-720x+1=0
a = -20; b = -720; c = +1;
Δ = b2-4ac
Δ = -7202-4·(-20)·1
Δ = 518480
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{518480}=\sqrt{16*32405}=\sqrt{16}*\sqrt{32405}=4\sqrt{32405}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-720)-4\sqrt{32405}}{2*-20}=\frac{720-4\sqrt{32405}}{-40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-720)+4\sqrt{32405}}{2*-20}=\frac{720+4\sqrt{32405}}{-40} $
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