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1/2x-3x=13
We move all terms to the left:
1/2x-3x-(13)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-3x+1/2x-13=0
We multiply all the terms by the denominator
-3x*2x-13*2x+1=0
Wy multiply elements
-6x^2-26x+1=0
a = -6; b = -26; c = +1;
Δ = b2-4ac
Δ = -262-4·(-6)·1
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-10\sqrt{7}}{2*-6}=\frac{26-10\sqrt{7}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+10\sqrt{7}}{2*-6}=\frac{26+10\sqrt{7}}{-12} $
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